# University of Florida/Eml4507/Team 7 Report 6

## Problem 1

On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.


### Find

Solve the general eigenvalue problem by first converting it to the standard eigenvalue problem for the spring-mass-damper system given on p.53-13 of 'Fead.s13.sec.53b'.

### Given

${\displaystyle M={\begin{pmatrix}3&0\\0&2\end{pmatrix}}}$

${\displaystyle K={\begin{pmatrix}30&-20\\-20&35\end{pmatrix}}}$

### Solution

Converting the general eigenvalue problem to the standard eigenvalue problem and solving it

General eigenvalue form:

${\displaystyle Kx=\lambda Mx}$

Standard eigenvalue form:

${\displaystyle K^{*}x^{*}=\lambda x^{*}}$

Where,
${\displaystyle K^{*}=M^{-1/2}KM^{-1/2}}$
${\displaystyle x^{*}=M^{1/2}x}$

${\displaystyle K^{*}={\begin{pmatrix}10&-8.16\\-8.16&17.5\end{pmatrix}}}$

${\displaystyle M^{1/2}={\begin{pmatrix}{\sqrt {3}}&0\\0&{\sqrt {2}}\end{pmatrix}}}$

${\displaystyle M^{-1/2}={\begin{pmatrix}1/{\sqrt {3}}&0\\0&1/{\sqrt {2}}\end{pmatrix}}}$

${\displaystyle K^{*}x^{*}=\lambda x^{*}}$

${\displaystyle K^{*}M^{1/2}x=\lambda M^{1/2}x}$

${\displaystyle \lambda M^{1/2}x-K^{*}M^{1/2}x=0}$
${\displaystyle (\lambda M^{1/2}-K^{*}M^{1/2})x=0}$

${\displaystyle \lambda M^{1/2}-K^{*}M^{1/2}={\begin{pmatrix}{\sqrt {3}}\lambda -17.3&11.5\\14.1&{\sqrt {2}}\lambda -24.7\end{pmatrix}}}$

${\displaystyle det(\lambda M^{1/2}-K^{*}M^{1/2})=0}$

Calculating the determinant
${\displaystyle ({\sqrt {3}}\lambda -17.3)({\sqrt {2}}\lambda -24.7)-162.15=0}$
${\displaystyle 2.4\lambda ^{2}-67.2\lambda +427.3=0}$

Therefore, the Eigenvalues are: ${\displaystyle \lambda _{1}=18.2,\lambda _{2}=9.8}$

The next step is finding the Eigenvectors
${\displaystyle \lambda _{1}=18.2}$
${\displaystyle (\lambda _{1}M^{1/2}-K^{*}M^{1/2})X_{1}={\begin{pmatrix}14.2&11.5\\14.1&1\end{pmatrix}}{\begin{pmatrix}x_{11}\\x_{21}\end{pmatrix}}={\begin{pmatrix}0\\0\end{pmatrix}}}$

Letting ${\displaystyle x_{21}=1}$ and calculating ${\displaystyle x_{12}}$

 ${\displaystyle {\begin{pmatrix}x_{11}\\x_{21}\end{pmatrix}}={\begin{pmatrix}-0.81\\1\end{pmatrix}}}$


${\displaystyle \lambda _{2}=9.8}$
${\displaystyle (\lambda _{2}M^{1/2}-K^{*}M^{1/2})X_{1}={\begin{pmatrix}-0.326&11.5\\14.1&-10.8\end{pmatrix}}{\begin{pmatrix}x_{12}\\x_{22}\end{pmatrix}}={\begin{pmatrix}0\\0\end{pmatrix}}}$

Letting ${\displaystyle x_{12}=1}$ and calculating ${\displaystyle x_{22}}$

 ${\displaystyle {\begin{pmatrix}x_{12}\\x_{22}\end{pmatrix}}={\begin{pmatrix}1\\1.3\end{pmatrix}}}$


${\displaystyle \mathbf {|X_{1}X_{2}|} ={\begin{bmatrix}x_{11}&x_{12}\\x_{21}&x_{22}\\\end{bmatrix}}={\begin{bmatrix}-0.81&1\\1&1.3\\\end{bmatrix}}}$


These results compare favorably with those from problem 5.6 using CALFEM.

Mass Orthogonality: ${\displaystyle x_{i}^{T}M_{xj}=0}$
The eigenvectors are therefore proven to be mass-orthogonal.

## Problem 2

On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.

### Find

The Lowest 3 eigenpairs ${\displaystyle (\omega _{j},\phi _{j})forj=1,2,3}$ by transforming the generalized eigenvalue problem into a standard eigenvalue problem and plot the 3 lowest mode shapes in a gif image.

### Given

${\displaystyle E=100GPa,A=1.0cm^{2},L=0.3m,\rho =5000{\frac {kg}{m^{3}}}}$

### Solution


clear
clc

%GIVENS
L=0.3;
E=100e9;
A=1e-4;
rho=5000;
ep=[E A];

%ELEMENT DOF
Edof=zeros(25,5);
for i=1:6
j=2*(i-1);
Edof(i,:)=[i,1+j,2+j,3+j,4+j];
end
for i=7:12
j=2*(i+1);
Edof(i,:)=[i,j-1,j,j+1,j+2];
end
for i=13:19
j=2*(i-13);
Edof(i,:)=[i,1+j,2+j,15+j,16+j];
end
for i=20:25
j=2*(i-20);
Edof(i,:)=[i,1+j,2+j,17+j,18+j];
end

%COORDINATES
ex=zeros(14,2);
ey=zeros(14,2);
for i=1:25
if i<7
ex(i,:)=[L*(i-1),L*i];
ey(i,:)=[0,0];
elseif i>6&&i<13
ex(i,:)=[L*(i-7),L*(i-6)];
ey(i,:)=[L,L];
elseif i>12&&i<20
ex(i,:)=[L*(i-13),L*(i-13)];
ey(i,:)=[0,L];
else
ex(i,:)=[L*(i-20),L*(i-19)];
ey(i,:)=[0,L];
end
end

%STIFFNESS AND MASS MATRIX
K=zeros(28);
M=zeros(28);
for i=1:25
E=ep(1);A=ep(2);
xt=ex(i,2)-ex(i,1);
yt=ey(i,2)-ey(i,1);
L=sqrt(xt^2+yt^2);
l=xt/L; m=yt/L;
ke=E*A/L*[l^2 l*m -l^2 -l*m;
l*m m^2 -l*m -m^2;
-l^2 -l*m l^2 l*m;
-l*m -m^2 l*m m^2;];
m=L*A*rho;
me=[m/2 0 0 0;
0 m/2 0 0;
0 0 m/2 0;
0 0 0 m/2];
edoft=Edof(i,2:5);
K(edoft,edoft)=K(edoft,edoft)+ke;
M(edoft,edoft)=M(edoft,edoft)+me;
end

%FIND THE EIGEN VALUES AND VECTORS
ndof=size(K,1);
freedof=[1:ndof]';
fixdof=[1 15 16]';
freedof(fixdof(:))=[];
Kred=K(freedof,freedof);
Mred=M(freedof,freedof);

Ks=Mred^(-1/2)*Kred*Mred^(-1/2);
[X1,D1]=eig(Ks);
X2=Mred^(-1/2)*X1;
for j=1:size(X2)
d=sqrt(X2(:,j)'*X2(:,j));
X3(:,j)=X2(:,j)/d;
end
[D1,i]=sort(diag(D1));
X4=X3(:,i);
eigenval=D1;
eigenvec=zeros(size(K,1),size(X4,1));
eigenvec(freedof,:)=X4;

%PLOT THE GIF
for kk=1:3
eigenvalx=eigenval(kk);
eigenvecx=eigenvec(:,kk);
w=sqrt(eigenvalx);
T=2*pi/w
dt=T/100;
t=0:dt:T;
figure(kk)

if kk==1;
filename = 'mode1 r5p2.gif';
elseif kk==2;
filename = 'mode2 r5p2.gif';
elseif kk==3;
filename = 'mode3 r5p2.gif';
end

for jj = 1:100
tt=t(jj);
d=eigenvecx*sin(w*tt);
d=d';
rr=Edof(:,2:5);
ed=zeros(25,4);
for i=1:25;
ed(i,1:4)=d(rr(i,:));
end
xd=(ex+ed(:,[1 3]))';
yd=(ey+ed(:,[2 4]))';
s1=['-' , 'k'];
axis manual
plot(xd,yd,s1)
set(gca, 'ylim', [-1.5 1.5], 'xlim', [0 3]);
drawnow
frame = getframe(1);
im = frame2im(frame);
[imind,cm] = rgb2ind(im,256);
if jj == 1;
imwrite(imind,cm,filename,'gif', 'Loopcount',inf);
else
imwrite(imind,cm,filename,'gif','WriteMode','append');
end
end
end


The resulting egienpairs are:

{\displaystyle \displaystyle {\begin{aligned}&\omega _{1}=1.6890\times 10^{5}\phi _{1}={\begin{bmatrix}0\\-0.0082\\-0.0279\\-0.0757\\-0.0479\\-0.1982\\-0.0605\\-0.3581\\-0.0670\\-0.5384\\-0.0690\\-0.7244\\-0.0690\\-0.9052\\0\\0\\0.0364\\-0.0677\\0.0645\\-0.1906\\0.0847\\-0.3514\\0.0974\\-0.5332\\0.1038\\-0.7213\\0.1058\\-0.9045\end{bmatrix}}\\&\omega _{2}=2.6676\times 10^{6}\phi _{2}={\begin{bmatrix}0\\-0.0745\\0.0227\\-0.4176\\0.0973\\-0.6512\\0.1884\\-0.6252\\0.2603\\-0.3137\\0.2941\\0.1825\\0.2976\\0.6937\\0\\0\\0.0732\\-0.3541\\0.0714\\-0.6149\\0.0153\\-0.6228\\-0.0603\\-0.3368\\-0.1201\\0.1553\\-0.1455\\0.6853\end{bmatrix}}\\&\omega _{3}=7.0219\times 10^{6}\phi _{3}={\begin{bmatrix}0\\-0.0352\\-0.2178\\-0.0416\\-0.3907\\-0.1023\\-0.5191\\-0.1283\\-0.6115\\-0.0751\\-0.6722\\0.0253\\-0.6941\\0.0971\\0\\0\\-0.1204\\-0.0089\\-0.2656\\-0.0780\\-0.4221\\-0.1195\\-0.5663\\-0.0809\\-0.6710\\0.0154\\-0.7178\\0.0940\end{bmatrix}}\\\end{aligned}}}

The mode shapes for the previous eigenpairs are"

## Problem 3

On our honor, the solution to this problem was generated by referring to the solution to Problem 3.1 at these locations: Eml4507 Team7 Report3,  Team Negative Damping (3): Report 3, Eml4507.s13.team2/Report3, and EML4507.s13.team4ever.R3. Their solutions were not copied, but consulted.


### Find

Using FE matlab code, with non-zero prescribed displacement degrees-of-freedom, using the same "connectivity array" given in the same problem statement, provide all of the unknown global displacement degrees-of-freedom, force components(reactions), and member forces. Plot the deformed shape superposed on the undeformed shape. Verify the results with CALFEM.

Compare the reactions in the case of non-zero prescribed disp dofs with the reactions in the case of zero prescribed disp dofs.

### Given

In the non-zero prescribed case:
${\displaystyle d_{1}=?cm}$
${\displaystyle d_{2}=?cm}$
${\displaystyle d_{3}=2cm}$
${\displaystyle d_{4}=-1cm}$
${\displaystyle d_{5}=-3cm}$
${\displaystyle d_{6}=5cm}$
${\displaystyle d_{7}=0cm}$
${\displaystyle d_{8}=0cm}$

In the zero prescribed case:
${\displaystyle d_{1}=?cm}$
${\displaystyle d_{2}=?cm}$
${\displaystyle d_{3}=0cm}$
${\displaystyle d_{4}=0cm}$
${\displaystyle d_{5}=0cm}$
${\displaystyle d_{6}=0cm}$
${\displaystyle d_{7}=0cm}$
${\displaystyle d_{8}=0cm}$

### Solution

MATLAB code:


%Displacements
d3= 0.02; %in m
d4= -0.01;
d5= -0.03;
d6= 0.05;
d7 = 0;
d8 = 0;
ph1= 0;
ph2 = 0;
dsmall = [d3; d4; d5; d6;]; %ph =placeholder, displacement unknown
theta=45;
%Property Matrix= [element number; EA/L; angle;];
P = [1:3; 10^5*206 10^5*206 10^5*206; -pi/6 pi/2 -5*pi/6;];
%angles refer to 1->3, 1->2, 1->4
%Global Coordinate System

GNC = [ 0, 0;
0, 1;
.866, -.5;
-.866, -.5;];

lm = [.866, -.5;
0   ,    1;
-.866, -.5;];

%populate global force matrix
dof = 8; %4 nodes, 2 directions reach
F = zeros(dof,1);
F(1) = 20000*cos(pi/4);
F(2) = 20000*sin(pi/4);

%populate stiffness matrices
lsq1 = (lm(1,1))^2;
msq1 = (lm(1,2))^2;
ltimesm1 = lm(1,1)*lm(1,2);
Ke1 = [ lsq1, ltimesm1, 0, 0, -lsq1, -ltimesm1, 0, 0;
ltimesm1, msq1, 0, 0 -ltimesm1, -msq1, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0;
-lsq1, -ltimesm1, 0, 0, lsq1, ltimesm1, 0, 0;
-ltimesm1, -msq1, 0, 0, ltimesm1, msq1, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0;];

lsq2 = (lm(2,1))^2;
msq2 = (lm(2,2))^2;
ltimesm2 = lm(2,1)*lm(2,2);
Ke2 = [ lsq2, ltimesm2, -lsq2, -ltimesm2, 0, 0, 0, 0;
ltimesm2, msq2, -ltimesm2, -msq2, 0, 0, 0, 0;
-lsq2, -ltimesm2, lsq2, ltimesm2, 0, 0, 0, 0;
-ltimesm2, -msq2, ltimesm2, msq2, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0;];

lsq3 = (lm(3,1))^2;
msq3 = (lm(3,2))^2;
ltimesm3 = lm(3,1)*lm(3,2);
Ke3 = [ lsq3, ltimesm3, 0, 0, 0, 0, -lsq3, -ltimesm3;
ltimesm3, msq3, 0, 0, 0, 0, -ltimesm3, -msq3;
0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0;
-lsq3, -ltimesm3, 0, 0, 0, 0, lsq3, ltimesm3;
-ltimesm3, -msq3, 0, 0, 0, 0, ltimesm3, msq3;];

Kglobal = P(2,1)*(Ke1+Ke2+Ke3)

%find unknown displacements, after reducing
Fsmall = [F(1) F(2)]';
Ksmall = zeros([2,6]);

for i=1:2
for j=1:6
Ksmall (i,j) = Kglobal((i+1),j);
end
end

unknownds = Ksmall\Fsmall
d1 = unknownds(1);
d2 = unknownds(2);

Ksmall2 = zeros([4,4]);

for i=1:4
for j=1:4
Ksmall2 (i,j) = Kglobal((i+1),j);
end
end

unknownFs = Ksmall2* dsmall

P1 = 10^5*206*.866*(d5-d1)-.5*(d6-d2)
P2 = 10^10*206*0*(d3-d1)-1*(d4-d2)
P3 = 10^10*206*-.866*(d7-d1)-.5*(d8-d2)


Resulting in:

Kglobal =

 Columns 1 through 7

  3.0898e+07            0            0            0  -1.5449e+07   8.9198e+06  -1.5449e+07
0     3.09e+07            0    -2.06e+07   8.9198e+06    -5.15e+06  -8.9198e+06
0            0            0            0            0            0            0
0    -2.06e+07            0     2.06e+07            0            0            0
-1.5449e+07   8.9198e+06            0            0   1.5449e+07  -8.9198e+06            0
8.9198e+06    -5.15e+06            0            0  -8.9198e+06     5.15e+06            0
-1.5449e+07  -8.9198e+06            0            0            0            0   1.5449e+07
-8.9198e+06    -5.15e+06            0            0            0            0   8.9198e+06

 Column 8

 -8.9198e+06
-5.15e+06
0
0
0
0
8.9198e+06
5.15e+06


unknownds =

  0.00045767
0.00045767

unknownFs =

  -1.339e+06
0
1.236e+06
-3.9818e+05


P1 =

 -5.3519e+05


P2 =

    1045.8


P3 =

    22.884


In the zero case: In the zero prescribed case:
${\displaystyle d_{1}=?cm}$
${\displaystyle d_{2}=?cm}$
${\displaystyle d_{3}=0cm}$
${\displaystyle d_{4}=0cm}$
${\displaystyle d_{5}=0cm}$
${\displaystyle d_{6}=0cm}$
${\displaystyle d_{7}=0cm}$
${\displaystyle d_{8}=0cm}$

Simply strike the rows and columns, resulting in:

unknownds =

  0.00045767
0.00045767


All the outer node reactions are zero, since their displacements are zero.

P1 =

 -0.34500e+05


P2 =

 -0.94400e+05


P3 =

 1.29000e+05


## Problem 4

On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.


### Find

Solve the initial truss structure using truss FEs

### Solution


function FEAr6p4

nodelocation=[-1.5 0 8;
1.5 0 8;
-1.5 1.5 4;
1.5 1.5 4;
1.5 -1.5 4;
-1.5 -1.5 4;
-4 4 0;
4 4 0;
4 -4 0;
-4 -4 0];

%INPUT:   ex = [-1.5 1.5]
%         ey = [0 0]         element node coordinates
%         ez = [z1 z2]
%
%         ep = [E A]           E: Young's modulus
%                              A: cross section area
%

ex=[nodelocation(1,1) nodelocation(2,1);
nodelocation(4,1) nodelocation(1,1);
nodelocation(3,1) nodelocation(2,1);
nodelocation(5,1) nodelocation(1,1);
nodelocation(6,1) nodelocation(2,1);
nodelocation(4,1) nodelocation(2,1);
nodelocation(5,1) nodelocation(2,1);
nodelocation(3,1) nodelocation(1,1);
nodelocation(6,1) nodelocation(1,1);
nodelocation(6,1) nodelocation(3,1);
nodelocation(5,1) nodelocation(4,1);
nodelocation(4,1) nodelocation(3,1);
nodelocation(6,1) nodelocation(5,1);
nodelocation(10,1) nodelocation(3,1);
nodelocation(7,1) nodelocation(6,1);
nodelocation(9,1) nodelocation(4,1);
nodelocation(8,1) nodelocation(5,1);
nodelocation(7,1) nodelocation(4,1);
nodelocation(8,1) nodelocation(3,1);
nodelocation(10,1) nodelocation(5,1);
nodelocation(9,1) nodelocation(6,1);
nodelocation(10,1) nodelocation(6,1);
nodelocation(7,1) nodelocation(3,1);
nodelocation(8,1) nodelocation(4,1);
nodelocation(9,1) nodelocation(5,1);];

ey=[nodelocation(1,2) nodelocation(2,2);
nodelocation(4,2) nodelocation(1,2);
nodelocation(3,2) nodelocation(2,2);
nodelocation(5,2) nodelocation(1,2);
nodelocation(6,2) nodelocation(2,2);
nodelocation(4,2) nodelocation(2,2);
nodelocation(5,2) nodelocation(2,2);
nodelocation(3,2) nodelocation(1,2);
nodelocation(6,2) nodelocation(1,2);
nodelocation(6,2) nodelocation(3,2);
nodelocation(5,2) nodelocation(4,2);
nodelocation(4,2) nodelocation(3,2);
nodelocation(6,2) nodelocation(5,2);
nodelocation(10,2) nodelocation(3,2);
nodelocation(7,2) nodelocation(6,2);
nodelocation(9,2) nodelocation(4,2);
nodelocation(8,2) nodelocation(5,2);
nodelocation(7,2) nodelocation(4,2);
nodelocation(8,2) nodelocation(3,2);
nodelocation(10,2) nodelocation(5,2);
nodelocation(9,2) nodelocation(6,2);
nodelocation(10,2) nodelocation(6,2);
nodelocation(7,2) nodelocation(3,2);
nodelocation(8,2) nodelocation(4,2);
nodelocation(9,2) nodelocation(5,2);];

ez=[nodelocation(1,3) nodelocation(2,3);
nodelocation(4,3) nodelocation(1,3);
nodelocation(3,3) nodelocation(2,3);
nodelocation(5,3) nodelocation(1,3);
nodelocation(6,3) nodelocation(2,3);
nodelocation(4,3) nodelocation(2,3);
nodelocation(5,3) nodelocation(2,3);
nodelocation(3,3) nodelocation(1,3);
nodelocation(6,3) nodelocation(1,3);
nodelocation(6,3) nodelocation(3,3);
nodelocation(5,3) nodelocation(4,3);
nodelocation(4,3) nodelocation(3,3);
nodelocation(6,3) nodelocation(5,3);
nodelocation(10,3) nodelocation(3,3);
nodelocation(7,3) nodelocation(6,3);
nodelocation(9,3) nodelocation(4,3);
nodelocation(8,3) nodelocation(5,3);
nodelocation(7,3) nodelocation(4,3);
nodelocation(8,3) nodelocation(3,3);
nodelocation(10,3) nodelocation(5,3);
nodelocation(9,3) nodelocation(6,3);
nodelocation(10,3) nodelocation(6,3);
nodelocation(7,3) nodelocation(3,3);
nodelocation(8,3) nodelocation(4,3);
nodelocation(9,3) nodelocation(5,3);];

E=3*10^7;  A=0.0218;

B=zeros(3, 25);
Kefinal=zeros(25,1);

for i=1:25

B(1,i)=ex(i,2)-ex(i,1) ;
B(2,i)= ey(i,2)-ey(i,1);
B(3,i)=ez(i,2)-ez(i,1) ;

for i=1:25
l=B(:,i);
L=sqrt(l'*l);
Kle=E*A/L*[1 -1;
-1  1];
n=l'/L
G=[   n   zeros(size(n));
zeros(size(n))   n   ];

Ke=G'*Kle*G

end
end

%  b=B*B'
%  L=sqrt(b)
% Kle=E*A/L*[1 -1;
%             -1  1];
%
%   n=B'/L;
%   G=[   n   zeros(size(n));
%     zeros(size(n))   n   ]
%
% Ke=G'*Kle*G;

OUTPUT:

Columns 1 through 4

1.0745   -2.3640    1.7192   -1.0745
-2.3640    5.2007   -3.7823    2.3640
1.7192   -3.7823    2.7508   -1.7192
-1.0745    2.3640   -1.7192    1.0745
2.3640   -5.2007    3.7823   -2.3640
-1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640   -1.7192
-5.2007    3.7823
3.7823   -2.7508
-2.3640    1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
0           0           0
0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689   -5.5171   -4.1378
2.0689    1.0345   -2.7585   -2.0689
-5.5171   -2.7585    7.3561    5.5171
-4.1378   -2.0689    5.5171    4.1378
-2.0689   -1.0345    2.7585    2.0689
5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689    5.5171
-1.0345    2.7585
2.7585   -7.3561
2.0689   -5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689    5.5171   -4.1378
-2.0689    1.0345   -2.7585    2.0689
5.5171   -2.7585    7.3561   -5.5171
-4.1378    2.0689   -5.5171    4.1378
2.0689   -1.0345    2.7585   -2.0689
-5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689   -5.5171
-1.0345    2.7585
2.7585   -7.3561
-2.0689    5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689   -5.5171   -4.1378
-2.0689    1.0345    2.7585    2.0689
-5.5171    2.7585    7.3561    5.5171
-4.1378    2.0689    5.5171    4.1378
2.0689   -1.0345   -2.7585   -2.0689
5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689    5.5171
-1.0345   -2.7585
-2.7585   -7.3561
-2.0689   -5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689    5.5171   -4.1378
2.0689    1.0345    2.7585   -2.0689
5.5171    2.7585    7.3561   -5.5171
-4.1378   -2.0689   -5.5171    4.1378
-2.0689   -1.0345   -2.7585    2.0689
-5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689   -5.5171
-1.0345   -2.7585
-2.7585   -7.3561
2.0689    5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
0   -0.1887    0.5033         0
0    0.5033   -1.3422         0

Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
0   -0.1887   -0.5033         0
0   -0.5033   -1.3422         0

Columns 5 through 6

0         0
-0.1887   -0.5033
-0.5033   -1.3422
0         0
0.1887    0.5033
0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
0   -0.1887    0.5033         0
0    0.5033   -1.3422         0

Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
0   -0.1887   -0.5033         0
0   -0.5033   -1.3422         0

Columns 5 through 6

0         0
-0.1887   -0.5033
-0.5033   -1.3422
0         0
0.1887    0.5033
0.5033    1.3422

Ke =

Columns 1 through 3

0           0           0
0      218000           0
0           0           0
0           0           0
0     -218000           0
0           0           0

Columns 4 through 6

0           0           0
0     -218000           0
0           0           0
0           0           0
0      218000           0
0           0           0

Ke =

Columns 1 through 3

0           0           0
0      218000           0
0           0           0
0           0           0
0     -218000           0
0           0           0

Columns 4 through 6

0           0           0
0     -218000           0
0           0           0
0           0           0
0      218000           0
0           0           0

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
0           0           0
0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
0           0           0
0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640    1.7192   -1.0745
2.3640    5.2007    3.7823   -2.3640
1.7192    3.7823    2.7508   -1.7192
-1.0745   -2.3640   -1.7192    1.0745
-2.3640   -5.2007   -3.7823    2.3640
-1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640   -1.7192
-5.2007   -3.7823
-3.7823   -2.7508
2.3640    1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640    1.7192   -1.0745
-2.3640    5.2007   -3.7823    2.3640
1.7192   -3.7823    2.7508   -1.7192
-1.0745    2.3640   -1.7192    1.0745
2.3640   -5.2007    3.7823   -2.3640
-1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640   -1.7192
-5.2007    3.7823
3.7823   -2.7508
-2.3640    1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640   -1.7192   -1.0745
-2.3640    5.2007    3.7823    2.3640
-1.7192    3.7823    2.7508    1.7192
-1.0745    2.3640    1.7192    1.0745
2.3640   -5.2007   -3.7823   -2.3640
1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640    1.7192
-5.2007   -3.7823
-3.7823   -2.7508
-2.3640   -1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
0           0           0
0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689   -5.5171   -4.1378
2.0689    1.0345   -2.7585   -2.0689
-5.5171   -2.7585    7.3561    5.5171
-4.1378   -2.0689    5.5171    4.1378
-2.0689   -1.0345    2.7585    2.0689
5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689    5.5171
-1.0345    2.7585
2.7585   -7.3561
2.0689   -5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689    5.5171   -4.1378
-2.0689    1.0345   -2.7585    2.0689
5.5171   -2.7585    7.3561   -5.5171
-4.1378    2.0689   -5.5171    4.1378
2.0689   -1.0345    2.7585   -2.0689
-5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689   -5.5171
-1.0345    2.7585
2.7585   -7.3561
-2.0689    5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689   -5.5171   -4.1378
-2.0689    1.0345    2.7585    2.0689
-5.5171    2.7585    7.3561    5.5171
-4.1378    2.0689    5.5171    4.1378
2.0689   -1.0345   -2.7585   -2.0689
5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689    5.5171
-1.0345   -2.7585
-2.7585   -7.3561
-2.0689   -5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689    5.5171   -4.1378
2.0689    1.0345    2.7585   -2.0689
5.5171    2.7585    7.3561   -5.5171
-4.1378   -2.0689   -5.5171    4.1378
-2.0689   -1.0345   -2.7585    2.0689
-5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689   -5.5171
-1.0345   -2.7585
-2.7585   -7.3561
2.0689    5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
0   -0.1887    0.5033         0
0    0.5033   -1.3422         0

Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
0   -0.1887   -0.5033         0
0   -0.5033   -1.3422         0

Columns 5 through 6

0         0
-0.1887   -0.5033
-0.5033   -1.3422
0         0
0.1887    0.5033
0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
0   -0.1887    0.5033         0
0    0.5033   -1.3422         0

Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
0   -0.1887   -0.5033         0
0   -0.5033   -1.3422         0

Columns 5 through 6

0         0
-0.1887   -0.5033
-0.5033   -1.3422
0         0
0.1887    0.5033
0.5033    1.3422

Ke =

Columns 1 through 3

0           0           0
0      218000           0
0           0           0
0           0           0
0     -218000           0
0           0           0

Columns 4 through 6

0           0           0
0     -218000           0
0           0           0
0           0           0
0      218000           0
0           0           0

Ke =

Columns 1 through 3

0           0           0
0      218000           0
0           0           0
0           0           0
0     -218000           0
0           0           0

Columns 4 through 6

0           0           0
0     -218000           0
0           0           0
0           0           0
0      218000           0
0           0           0

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
0           0           0
0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
0           0           0
0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640    1.7192   -1.0745
2.3640    5.2007    3.7823   -2.3640
1.7192    3.7823    2.7508   -1.7192
-1.0745   -2.3640   -1.7192    1.0745
-2.3640   -5.2007   -3.7823    2.3640
-1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640   -1.7192
-5.2007   -3.7823
-3.7823   -2.7508
2.3640    1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640    1.7192   -1.0745
-2.3640    5.2007   -3.7823    2.3640
1.7192   -3.7823    2.7508   -1.7192
-1.0745    2.3640   -1.7192    1.0745
2.3640   -5.2007    3.7823   -2.3640
-1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640   -1.7192
-5.2007    3.7823
3.7823   -2.7508
-2.3640    1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640   -1.7192   -1.0745
-2.3640    5.2007    3.7823    2.3640
-1.7192    3.7823    2.7508    1.7192
-1.0745    2.3640    1.7192    1.0745
2.3640   -5.2007   -3.7823   -2.3640
1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640    1.7192
-5.2007   -3.7823
-3.7823   -2.7508
-2.3640   -1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640   -1.7192   -1.0745
2.3640    5.2007   -3.7823   -2.3640
-1.7192   -3.7823    2.7508    1.7192
-1.0745   -2.3640    1.7192    1.0745
-2.3640   -5.2007    3.7823    2.3640
1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640    1.7192
-5.2007    3.7823
3.7823   -2.7508
2.3640   -1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
0           0           0
0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689   -5.5171   -4.1378
2.0689    1.0345   -2.7585   -2.0689
-5.5171   -2.7585    7.3561    5.5171
-4.1378   -2.0689    5.5171    4.1378
-2.0689   -1.0345    2.7585    2.0689
5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689    5.5171
-1.0345    2.7585
2.7585   -7.3561
2.0689   -5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689    5.5171   -4.1378
-2.0689    1.0345   -2.7585    2.0689
5.5171   -2.7585    7.3561   -5.5171
-4.1378    2.0689   -5.5171    4.1378
2.0689   -1.0345    2.7585   -2.0689
-5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689   -5.5171
-1.0345    2.7585
2.7585   -7.3561
-2.0689    5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689   -5.5171   -4.1378
-2.0689    1.0345    2.7585    2.0689
-5.5171    2.7585    7.3561    5.5171
-4.1378    2.0689    5.5171    4.1378
2.0689   -1.0345   -2.7585   -2.0689
5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689    5.5171
-1.0345   -2.7585
-2.7585   -7.3561
-2.0689   -5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689    5.5171   -4.1378
2.0689    1.0345    2.7585   -2.0689
5.5171    2.7585    7.3561   -5.5171
-4.1378   -2.0689   -5.5171    4.1378
-2.0689   -1.0345   -2.7585    2.0689
-5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689   -5.5171
-1.0345   -2.7585
-2.7585   -7.3561
2.0689    5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
0   -0.1887    0.5033         0
0    0.5033   -1.3422         0

Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
0   -0.1887   -0.5033         0
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Columns 5 through 6

0         0
-0.1887   -0.5033
-0.5033   -1.3422
0         0
0.1887    0.5033
0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
0   -0.1887    0.5033         0
0    0.5033   -1.3422         0

Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
0   -0.1887   -0.5033         0
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Columns 5 through 6

0         0
-0.1887   -0.5033
-0.5033   -1.3422
0         0
0.1887    0.5033
0.5033    1.3422

Ke =

Columns 1 through 3

0           0           0
0      218000           0
0           0           0
0           0           0
0     -218000           0
0           0           0

Columns 4 through 6

0           0           0
0     -218000           0
0           0           0
0           0           0
0      218000           0
0           0           0

Ke =

Columns 1 through 3

0           0           0
0      218000           0
0           0           0
0           0           0
0     -218000           0
0           0           0

Columns 4 through 6

0           0           0
0     -218000           0
0           0           0
0           0           0
0      218000           0
0           0           0

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
0           0           0
0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
0           0           0
0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640    1.7192   -1.0745
2.3640    5.2007    3.7823   -2.3640
1.7192    3.7823    2.7508   -1.7192
-1.0745   -2.3640   -1.7192    1.0745
-2.3640   -5.2007   -3.7823    2.3640
-1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640   -1.7192
-5.2007   -3.7823
-3.7823   -2.7508
2.3640    1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640    1.7192   -1.0745
-2.3640    5.2007   -3.7823    2.3640
1.7192   -3.7823    2.7508   -1.7192
-1.0745    2.3640   -1.7192    1.0745
2.3640   -5.2007    3.7823   -2.3640
-1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640   -1.7192
-5.2007    3.7823
3.7823   -2.7508
-2.3640    1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640   -1.7192   -1.0745
-2.3640    5.2007    3.7823    2.3640
-1.7192    3.7823    2.7508    1.7192
-1.0745    2.3640    1.7192    1.0745
2.3640   -5.2007   -3.7823   -2.3640
1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640    1.7192
-5.2007   -3.7823
-3.7823   -2.7508
-2.3640   -1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640   -1.7192   -1.0745
2.3640    5.2007   -3.7823   -2.3640
-1.7192   -3.7823    2.7508    1.7192
-1.0745   -2.3640    1.7192    1.0745
-2.3640   -5.2007    3.7823    2.3640
1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640    1.7192
-5.2007    3.7823
3.7823   -2.7508
2.3640   -1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640    3.7823   -5.2007
-2.3640    1.0745   -1.7192    2.3640
3.7823   -1.7192    2.7508   -3.7823
-5.2007    2.3640   -3.7823    5.2007
2.3640   -1.0745    1.7192   -2.3640
-3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640   -3.7823
-1.0745    1.7192
1.7192   -2.7508
-2.3640    3.7823
1.0745   -1.7192
-1.7192    2.7508

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
0           0           0
0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689   -5.5171   -4.1378
2.0689    1.0345   -2.7585   -2.0689
-5.5171   -2.7585    7.3561    5.5171
-4.1378   -2.0689    5.5171    4.1378
-2.0689   -1.0345    2.7585    2.0689
5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689    5.5171
-1.0345    2.7585
2.7585   -7.3561
2.0689   -5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689    5.5171   -4.1378
-2.0689    1.0345   -2.7585    2.0689
5.5171   -2.7585    7.3561   -5.5171
-4.1378    2.0689   -5.5171    4.1378
2.0689   -1.0345    2.7585   -2.0689
-5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689   -5.5171
-1.0345    2.7585
2.7585   -7.3561
-2.0689    5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689   -5.5171   -4.1378
-2.0689    1.0345    2.7585    2.0689
-5.5171    2.7585    7.3561    5.5171
-4.1378    2.0689    5.5171    4.1378
2.0689   -1.0345   -2.7585   -2.0689
5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689    5.5171
-1.0345   -2.7585
-2.7585   -7.3561
-2.0689   -5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689    5.5171   -4.1378
2.0689    1.0345    2.7585   -2.0689
5.5171    2.7585    7.3561   -5.5171
-4.1378   -2.0689   -5.5171    4.1378
-2.0689   -1.0345   -2.7585    2.0689
-5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689   -5.5171
-1.0345   -2.7585
-2.7585   -7.3561
2.0689    5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
0   -0.1887    0.5033         0
0    0.5033   -1.3422         0

Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
0   -0.1887   -0.5033         0
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Columns 5 through 6

0         0
-0.1887   -0.5033
-0.5033   -1.3422
0         0
0.1887    0.5033
0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
0   -0.1887    0.5033         0
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Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
0   -0.1887   -0.5033         0
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Columns 5 through 6

0         0
-0.1887   -0.5033
-0.5033   -1.3422
0         0
0.1887    0.5033
0.5033    1.3422

Ke =

Columns 1 through 3

0           0           0
0      218000           0
0           0           0
0           0           0
0     -218000           0
0           0           0

Columns 4 through 6

0           0           0
0     -218000           0
0           0           0
0           0           0
0      218000           0
0           0           0

Ke =

Columns 1 through 3

0           0           0
0      218000           0
0           0           0
0           0           0
0     -218000           0
0           0           0

Columns 4 through 6

0           0           0
0     -218000           0
0           0           0
0           0           0
0      218000           0
0           0           0

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
0           0           0
0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
0           0           0
0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640    1.7192   -1.0745
2.3640    5.2007    3.7823   -2.3640
1.7192    3.7823    2.7508   -1.7192
-1.0745   -2.3640   -1.7192    1.0745
-2.3640   -5.2007   -3.7823    2.3640
-1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640   -1.7192
-5.2007   -3.7823
-3.7823   -2.7508
2.3640    1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640    1.7192   -1.0745
-2.3640    5.2007   -3.7823    2.3640
1.7192   -3.7823    2.7508   -1.7192
-1.0745    2.3640   -1.7192    1.0745
2.3640   -5.2007    3.7823   -2.3640
-1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640   -1.7192
-5.2007    3.7823
3.7823   -2.7508
-2.3640    1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640   -1.7192   -1.0745
-2.3640    5.2007    3.7823    2.3640
-1.7192    3.7823    2.7508    1.7192
-1.0745    2.3640    1.7192    1.0745
2.3640   -5.2007   -3.7823   -2.3640
1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640    1.7192
-5.2007   -3.7823
-3.7823   -2.7508
-2.3640   -1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640   -1.7192   -1.0745
2.3640    5.2007   -3.7823   -2.3640
-1.7192   -3.7823    2.7508    1.7192
-1.0745   -2.3640    1.7192    1.0745
-2.3640   -5.2007    3.7823    2.3640
1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640    1.7192
-5.2007    3.7823
3.7823   -2.7508
2.3640   -1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640    3.7823   -5.2007
-2.3640    1.0745   -1.7192    2.3640
3.7823   -1.7192    2.7508   -3.7823
-5.2007    2.3640   -3.7823    5.2007
2.3640   -1.0745    1.7192   -2.3640
-3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640   -3.7823
-1.0745    1.7192
1.7192   -2.7508
-2.3640    3.7823
1.0745   -1.7192
-1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640   -3.7823   -5.2007
2.3640    1.0745   -1.7192   -2.3640
-3.7823   -1.7192    2.7508    3.7823
-5.2007   -2.3640    3.7823    5.2007
-2.3640   -1.0745    1.7192    2.3640
3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640    3.7823
-1.0745    1.7192
1.7192   -2.7508
2.3640   -3.7823
1.0745   -1.7192
-1.7192    2.7508

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
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0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
0           0           0
218000           0           0
0           0           0
0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689   -5.5171   -4.1378
2.0689    1.0345   -2.7585   -2.0689
-5.5171   -2.7585    7.3561    5.5171
-4.1378   -2.0689    5.5171    4.1378
-2.0689   -1.0345    2.7585    2.0689
5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689    5.5171
-1.0345    2.7585
2.7585   -7.3561
2.0689   -5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689    5.5171   -4.1378
-2.0689    1.0345   -2.7585    2.0689
5.5171   -2.7585    7.3561   -5.5171
-4.1378    2.0689   -5.5171    4.1378
2.0689   -1.0345    2.7585   -2.0689
-5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689   -5.5171
-1.0345    2.7585
2.7585   -7.3561
-2.0689    5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689   -5.5171   -4.1378
-2.0689    1.0345    2.7585    2.0689
-5.5171    2.7585    7.3561    5.5171
-4.1378    2.0689    5.5171    4.1378
2.0689   -1.0345   -2.7585   -2.0689
5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689    5.5171
-1.0345   -2.7585
-2.7585   -7.3561
-2.0689   -5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689    5.5171   -4.1378
2.0689    1.0345    2.7585   -2.0689
5.5171    2.7585    7.3561   -5.5171
-4.1378   -2.0689   -5.5171    4.1378
-2.0689   -1.0345   -2.7585    2.0689
-5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689   -5.5171
-1.0345   -2.7585
-2.7585   -7.3561
2.0689    5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
0   -0.1887    0.5033         0
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Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
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0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
0   -0.1887   -0.5033         0
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Columns 5 through 6

0         0
-0.1887   -0.5033
-0.5033   -1.3422
0         0
0.1887    0.5033
0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
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Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
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0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
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Columns 5 through 6

0         0
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0.1887    0.5033
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Ke =

Columns 1 through 3

0           0           0
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Columns 4 through 6

0           0           0
0     -218000           0
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0      218000           0
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Ke =

Columns 1 through 3

0           0           0
0      218000           0
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0     -218000           0
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Columns 4 through 6

0           0           0
0     -218000           0
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Ke =

Columns 1 through 3

218000           0           0
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Columns 4 through 6

-218000           0           0
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218000           0           0
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Ke =

Columns 1 through 3

218000           0           0
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Columns 4 through 6

-218000           0           0
0           0           0
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218000           0           0
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Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640    1.7192   -1.0745
2.3640    5.2007    3.7823   -2.3640
1.7192    3.7823    2.7508   -1.7192
-1.0745   -2.3640   -1.7192    1.0745
-2.3640   -5.2007   -3.7823    2.3640
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Columns 5 through 6

-2.3640   -1.7192
-5.2007   -3.7823
-3.7823   -2.7508
2.3640    1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640    1.7192   -1.0745
-2.3640    5.2007   -3.7823    2.3640
1.7192   -3.7823    2.7508   -1.7192
-1.0745    2.3640   -1.7192    1.0745
2.3640   -5.2007    3.7823   -2.3640
-1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640   -1.7192
-5.2007    3.7823
3.7823   -2.7508
-2.3640    1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640   -1.7192   -1.0745
-2.3640    5.2007    3.7823    2.3640
-1.7192    3.7823    2.7508    1.7192
-1.0745    2.3640    1.7192    1.0745
2.3640   -5.2007   -3.7823   -2.3640
1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640    1.7192
-5.2007   -3.7823
-3.7823   -2.7508
-2.3640   -1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640   -1.7192   -1.0745
2.3640    5.2007   -3.7823   -2.3640
-1.7192   -3.7823    2.7508    1.7192
-1.0745   -2.3640    1.7192    1.0745
-2.3640   -5.2007    3.7823    2.3640
1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640    1.7192
-5.2007    3.7823
3.7823   -2.7508
2.3640   -1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640    3.7823   -5.2007
-2.3640    1.0745   -1.7192    2.3640
3.7823   -1.7192    2.7508   -3.7823
-5.2007    2.3640   -3.7823    5.2007
2.3640   -1.0745    1.7192   -2.3640
-3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640   -3.7823
-1.0745    1.7192
1.7192   -2.7508
-2.3640    3.7823
1.0745   -1.7192
-1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640   -3.7823   -5.2007
2.3640    1.0745   -1.7192   -2.3640
-3.7823   -1.7192    2.7508    3.7823
-5.2007   -2.3640    3.7823    5.2007
-2.3640   -1.0745    1.7192    2.3640
3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640    3.7823
-1.0745    1.7192
1.7192   -2.7508
2.3640   -3.7823
1.0745   -1.7192
-1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640    3.7823   -5.2007
2.3640    1.0745    1.7192   -2.3640
3.7823    1.7192    2.7508   -3.7823
-5.2007   -2.3640   -3.7823    5.2007
-2.3640   -1.0745   -1.7192    2.3640
-3.7823   -1.7192   -2.7508    3.7823

Columns 5 through 6

-2.3640   -3.7823
-1.0745   -1.7192
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2.3640    3.7823
1.0745    1.7192
1.7192    2.7508

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
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Columns 4 through 6

-218000           0           0
0           0           0
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218000           0           0
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0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689   -5.5171   -4.1378
2.0689    1.0345   -2.7585   -2.0689
-5.5171   -2.7585    7.3561    5.5171
-4.1378   -2.0689    5.5171    4.1378
-2.0689   -1.0345    2.7585    2.0689
5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689    5.5171
-1.0345    2.7585
2.7585   -7.3561
2.0689   -5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689    5.5171   -4.1378
-2.0689    1.0345   -2.7585    2.0689
5.5171   -2.7585    7.3561   -5.5171
-4.1378    2.0689   -5.5171    4.1378
2.0689   -1.0345    2.7585   -2.0689
-5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689   -5.5171
-1.0345    2.7585
2.7585   -7.3561
-2.0689    5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689   -5.5171   -4.1378
-2.0689    1.0345    2.7585    2.0689
-5.5171    2.7585    7.3561    5.5171
-4.1378    2.0689    5.5171    4.1378
2.0689   -1.0345   -2.7585   -2.0689
5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689    5.5171
-1.0345   -2.7585
-2.7585   -7.3561
-2.0689   -5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689    5.5171   -4.1378
2.0689    1.0345    2.7585   -2.0689
5.5171    2.7585    7.3561   -5.5171
-4.1378   -2.0689   -5.5171    4.1378
-2.0689   -1.0345   -2.7585    2.0689
-5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689   -5.5171
-1.0345   -2.7585
-2.7585   -7.3561
2.0689    5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
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Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
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Columns 5 through 6

0         0
-0.1887   -0.5033
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0.1887    0.5033
0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
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Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
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Columns 5 through 6

0         0
-0.1887   -0.5033
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0.1887    0.5033
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Ke =

Columns 1 through 3

0           0           0
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Columns 4 through 6

0           0           0
0     -218000           0
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Ke =

Columns 1 through 3

0           0           0
0      218000           0
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0           0           0
0     -218000           0
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Columns 4 through 6

0           0           0
0     -218000           0
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Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
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Columns 4 through 6

-218000           0           0
0           0           0
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218000           0           0
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Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
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Columns 4 through 6

-218000           0           0
0           0           0
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218000           0           0
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Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640    1.7192   -1.0745
2.3640    5.2007    3.7823   -2.3640
1.7192    3.7823    2.7508   -1.7192
-1.0745   -2.3640   -1.7192    1.0745
-2.3640   -5.2007   -3.7823    2.3640
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Columns 5 through 6

-2.3640   -1.7192
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2.3640    1.7192
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3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640    1.7192   -1.0745
-2.3640    5.2007   -3.7823    2.3640
1.7192   -3.7823    2.7508   -1.7192
-1.0745    2.3640   -1.7192    1.0745
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Columns 5 through 6

2.3640   -1.7192
-5.2007    3.7823
3.7823   -2.7508
-2.3640    1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640   -1.7192   -1.0745
-2.3640    5.2007    3.7823    2.3640
-1.7192    3.7823    2.7508    1.7192
-1.0745    2.3640    1.7192    1.0745
2.3640   -5.2007   -3.7823   -2.3640
1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640    1.7192
-5.2007   -3.7823
-3.7823   -2.7508
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5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640   -1.7192   -1.0745
2.3640    5.2007   -3.7823   -2.3640
-1.7192   -3.7823    2.7508    1.7192
-1.0745   -2.3640    1.7192    1.0745
-2.3640   -5.2007    3.7823    2.3640
1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640    1.7192
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3.7823   -2.7508
2.3640   -1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640    3.7823   -5.2007
-2.3640    1.0745   -1.7192    2.3640
3.7823   -1.7192    2.7508   -3.7823
-5.2007    2.3640   -3.7823    5.2007
2.3640   -1.0745    1.7192   -2.3640
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Columns 5 through 6

2.3640   -3.7823
-1.0745    1.7192
1.7192   -2.7508
-2.3640    3.7823
1.0745   -1.7192
-1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640   -3.7823   -5.2007
2.3640    1.0745   -1.7192   -2.3640
-3.7823   -1.7192    2.7508    3.7823
-5.2007   -2.3640    3.7823    5.2007
-2.3640   -1.0745    1.7192    2.3640
3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640    3.7823
-1.0745    1.7192
1.7192   -2.7508
2.3640   -3.7823
1.0745   -1.7192
-1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640    3.7823   -5.2007
2.3640    1.0745    1.7192   -2.3640
3.7823    1.7192    2.7508   -3.7823
-5.2007   -2.3640   -3.7823    5.2007
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Columns 5 through 6

-2.3640   -3.7823
-1.0745   -1.7192
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2.3640    3.7823
1.0745    1.7192
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Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640   -3.7823   -5.2007
-2.3640    1.0745    1.7192    2.3640
-3.7823    1.7192    2.7508    3.7823
-5.2007    2.3640    3.7823    5.2007
2.3640   -1.0745   -1.7192   -2.3640
3.7823   -1.7192   -2.7508   -3.7823

Columns 5 through 6

2.3640    3.7823
-1.0745   -1.7192
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-2.3640   -3.7823
1.0745    1.7192
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Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000           0           0
0           0           0
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-218000           0           0
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Columns 4 through 6

-218000           0           0
0           0           0
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218000           0           0
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0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689   -5.5171   -4.1378
2.0689    1.0345   -2.7585   -2.0689
-5.5171   -2.7585    7.3561    5.5171
-4.1378   -2.0689    5.5171    4.1378
-2.0689   -1.0345    2.7585    2.0689
5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689    5.5171
-1.0345    2.7585
2.7585   -7.3561
2.0689   -5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689    5.5171   -4.1378
-2.0689    1.0345   -2.7585    2.0689
5.5171   -2.7585    7.3561   -5.5171
-4.1378    2.0689   -5.5171    4.1378
2.0689   -1.0345    2.7585   -2.0689
-5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689   -5.5171
-1.0345    2.7585
2.7585   -7.3561
-2.0689    5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689   -5.5171   -4.1378
-2.0689    1.0345    2.7585    2.0689
-5.5171    2.7585    7.3561    5.5171
-4.1378    2.0689    5.5171    4.1378
2.0689   -1.0345   -2.7585   -2.0689
5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689    5.5171
-1.0345   -2.7585
-2.7585   -7.3561
-2.0689   -5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689    5.5171   -4.1378
2.0689    1.0345    2.7585   -2.0689
5.5171    2.7585    7.3561   -5.5171
-4.1378   -2.0689   -5.5171    4.1378
-2.0689   -1.0345   -2.7585    2.0689
-5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689   -5.5171
-1.0345   -2.7585
-2.7585   -7.3561
2.0689    5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
0   -0.1887    0.5033         0
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Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
0   -0.1887   -0.5033         0
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Columns 5 through 6

0         0
-0.1887   -0.5033
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0         0
0.1887    0.5033
0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
0   -0.1887    0.5033         0
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Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
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Columns 5 through 6

0         0
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0.1887    0.5033
0.5033    1.3422

Ke =

Columns 1 through 3

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Columns 4 through 6

0           0           0
0     -218000           0
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Ke =

Columns 1 through 3

0           0           0
0      218000           0
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Columns 4 through 6

0           0           0
0     -218000           0
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0      218000           0
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Ke =

Columns 1 through 3

218000           0           0
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Columns 4 through 6

-218000           0           0
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218000           0           0
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Ke =

Columns 1 through 3

218000           0           0
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Columns 4 through 6

-218000           0           0
0           0           0
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218000           0           0
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Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640    1.7192   -1.0745
2.3640    5.2007    3.7823   -2.3640
1.7192    3.7823    2.7508   -1.7192
-1.0745   -2.3640   -1.7192    1.0745
-2.3640   -5.2007   -3.7823    2.3640
-1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640   -1.7192
-5.2007   -3.7823
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2.3640    1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640    1.7192   -1.0745
-2.3640    5.2007   -3.7823    2.3640
1.7192   -3.7823    2.7508   -1.7192
-1.0745    2.3640   -1.7192    1.0745
2.3640   -5.2007    3.7823   -2.3640
-1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640   -1.7192
-5.2007    3.7823
3.7823   -2.7508
-2.3640    1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640   -1.7192   -1.0745
-2.3640    5.2007    3.7823    2.3640
-1.7192    3.7823    2.7508    1.7192
-1.0745    2.3640    1.7192    1.0745
2.3640   -5.2007   -3.7823   -2.3640
1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640    1.7192
-5.2007   -3.7823
-3.7823   -2.7508
-2.3640   -1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640   -1.7192   -1.0745
2.3640    5.2007   -3.7823   -2.3640
-1.7192   -3.7823    2.7508    1.7192
-1.0745   -2.3640    1.7192    1.0745
-2.3640   -5.2007    3.7823    2.3640
1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640    1.7192
-5.2007    3.7823
3.7823   -2.7508
2.3640   -1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640    3.7823   -5.2007
-2.3640    1.0745   -1.7192    2.3640
3.7823   -1.7192    2.7508   -3.7823
-5.2007    2.3640   -3.7823    5.2007
2.3640   -1.0745    1.7192   -2.3640
-3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640   -3.7823
-1.0745    1.7192
1.7192   -2.7508
-2.3640    3.7823
1.0745   -1.7192
-1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640   -3.7823   -5.2007
2.3640    1.0745   -1.7192   -2.3640
-3.7823   -1.7192    2.7508    3.7823
-5.2007   -2.3640    3.7823    5.2007
-2.3640   -1.0745    1.7192    2.3640
3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640    3.7823
-1.0745    1.7192
1.7192   -2.7508
2.3640   -3.7823
1.0745   -1.7192
-1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640    3.7823   -5.2007
2.3640    1.0745    1.7192   -2.3640
3.7823    1.7192    2.7508   -3.7823
-5.2007   -2.3640   -3.7823    5.2007
-2.3640   -1.0745   -1.7192    2.3640
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Columns 5 through 6

-2.3640   -3.7823
-1.0745   -1.7192
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2.3640    3.7823
1.0745    1.7192
1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640   -3.7823   -5.2007
-2.3640    1.0745    1.7192    2.3640
-3.7823    1.7192    2.7508    3.7823
-5.2007    2.3640    3.7823    5.2007
2.3640   -1.0745   -1.7192   -2.3640
3.7823   -1.7192   -2.7508   -3.7823

Columns 5 through 6

2.3640    3.7823
-1.0745   -1.7192
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-2.3640   -3.7823
1.0745    1.7192
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Ke =

1.0e+004 *

Columns 1 through 4

2.6865    2.6865    4.2984   -2.6865
2.6865    2.6865    4.2984   -2.6865
4.2984    4.2984    6.8775   -4.2984
-2.6865   -2.6865   -4.2984    2.6865
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Columns 5 through 6

-2.6865   -4.2984
-2.6865   -4.2984
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2.6865    4.2984
2.6865    4.2984
4.2984    6.8775

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
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Columns 4 through 6

-218000           0           0
0           0           0
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218000           0           0
0           0           0
0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689   -5.5171   -4.1378
2.0689    1.0345   -2.7585   -2.0689
-5.5171   -2.7585    7.3561    5.5171
-4.1378   -2.0689    5.5171    4.1378
-2.0689   -1.0345    2.7585    2.0689
5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689    5.5171
-1.0345    2.7585
2.7585   -7.3561
2.0689   -5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689    5.5171   -4.1378
-2.0689    1.0345   -2.7585    2.0689
5.5171   -2.7585    7.3561   -5.5171
-4.1378    2.0689   -5.5171    4.1378
2.0689   -1.0345    2.7585   -2.0689
-5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689   -5.5171
-1.0345    2.7585
2.7585   -7.3561
-2.0689    5.5171
1.0345   -2.7585
-2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689   -5.5171   -4.1378
-2.0689    1.0345    2.7585    2.0689
-5.5171    2.7585    7.3561    5.5171
-4.1378    2.0689    5.5171    4.1378
2.0689   -1.0345   -2.7585   -2.0689
5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689    5.5171
-1.0345   -2.7585
-2.7585   -7.3561
-2.0689   -5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689    5.5171   -4.1378
2.0689    1.0345    2.7585   -2.0689
5.5171    2.7585    7.3561   -5.5171
-4.1378   -2.0689   -5.5171    4.1378
-2.0689   -1.0345   -2.7585    2.0689
-5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689   -5.5171
-1.0345   -2.7585
-2.7585   -7.3561
2.0689    5.5171
1.0345    2.7585
2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
0   -0.1887    0.5033         0
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Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
0   -0.1887   -0.5033         0
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Columns 5 through 6

0         0
-0.1887   -0.5033
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0         0
0.1887    0.5033
0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
0   -0.5033    1.3422         0
0         0         0         0
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Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
0         0
0.1887   -0.5033
-0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
0    0.5033    1.3422         0
0         0         0         0
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Columns 5 through 6

0         0
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0.1887    0.5033
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Ke =

Columns 1 through 3

0           0           0
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Columns 4 through 6

0           0           0
0     -218000           0
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0      218000           0
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Ke =

Columns 1 through 3

0           0           0
0      218000           0
0           0           0
0           0           0
0     -218000           0
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Columns 4 through 6

0           0           0
0     -218000           0
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0      218000           0
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Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
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Columns 4 through 6

-218000           0           0
0           0           0
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218000           0           0
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Ke =

Columns 1 through 3

218000           0           0
0           0           0
0           0           0
-218000           0           0
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0           0           0

Columns 4 through 6

-218000           0           0
0           0           0
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218000           0           0
0           0           0
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Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640    1.7192   -1.0745
2.3640    5.2007    3.7823   -2.3640
1.7192    3.7823    2.7508   -1.7192
-1.0745   -2.3640   -1.7192    1.0745
-2.3640   -5.2007   -3.7823    2.3640
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Columns 5 through 6

-2.3640   -1.7192
-5.2007   -3.7823
-3.7823   -2.7508
2.3640    1.7192
5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640    1.7192   -1.0745
-2.3640    5.2007   -3.7823    2.3640
1.7192   -3.7823    2.7508   -1.7192
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2.3640   -5.2007    3.7823   -2.3640
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Columns 5 through 6

2.3640   -1.7192
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3.7823   -2.7508
-2.3640    1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640   -1.7192   -1.0745
-2.3640    5.2007    3.7823    2.3640
-1.7192    3.7823    2.7508    1.7192
-1.0745    2.3640    1.7192    1.0745
2.3640   -5.2007   -3.7823   -2.3640
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Columns 5 through 6

2.3640    1.7192
-5.2007   -3.7823
-3.7823   -2.7508
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5.2007    3.7823
3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640   -1.7192   -1.0745
2.3640    5.2007   -3.7823   -2.3640
-1.7192   -3.7823    2.7508    1.7192
-1.0745   -2.3640    1.7192    1.0745
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1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640    1.7192
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3.7823   -2.7508
2.3640   -1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640    3.7823   -5.2007
-2.3640    1.0745   -1.7192    2.3640
3.7823   -1.7192    2.7508   -3.7823
-5.2007    2.3640   -3.7823    5.2007
2.3640   -1.0745    1.7192   -2.3640
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Columns 5 through 6

2.3640   -3.7823
-1.0745    1.7192
1.7192   -2.7508
-2.3640    3.7823
1.0745   -1.7192
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Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640   -3.7823   -5.2007
2.3640    1.0745   -1.7192   -2.3640
-3.7823   -1.7192    2.7508    3.7823
-5.2007   -2.3640    3.7823    5.2007
-2.3640   -1.0745    1.7192    2.3640
3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640    3.7823
-1.0745    1.7192
1.7192   -2.7508
2.3640   -3.7823
1.0745   -1.7192
-1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640    3.7823   -5.2007
2.3640    1.0745    1.7192   -2.3640
3.7823    1.7192    2.7508   -3.7823
-5.2007   -2.3640   -3.7823    5.2007
-2.3640   -1.0745   -1.7192    2.3640
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Columns 5 through 6

-2.3640   -3.7823
-1.0745   -1.7192
-1.7192   -2.7508
2.3640    3.7823
1.0745    1.7192
1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640   -3.7823   -5.2007
-2.3640    1.0745    1.7192    2.3640
-3.7823    1.7192    2.7508    3.7823
-5.2007    2.3640    3.7823    5.2007
2.3640   -1.0745   -1.7192   -2.3640
3.7823   -1.7192   -2.7508   -3.7823

Columns 5 through 6

2.3640    3.7823
-1.0745   -1.7192
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-2.3640   -3.7823
1.0745    1.7192
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Ke =

1.0e+004 *

Columns 1 through 4

2.6865    2.6865    4.2984   -2.6865
2.6865    2.6865    4.2984   -2.6865
4.2984    4.2984    6.8775   -4.2984
-2.6865   -2.6865   -4.2984    2.6865
-2.6865   -2.6865   -4.2984    2.6865
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Columns 5 through 6

-2.6865   -4.2984
-2.6865   -4.2984
-4.2984   -6.8775
2.6865    4.2984
2.6865    4.2984
4.2984    6.8775

Ke =

1.0e+004 *

Columns 1 through 4

2.6865   -2.6865    4.2984   -2.6865
-2.6865    2.6865   -4.2984    2.6865
4.2984   -4.2984    6.8775   -4.2984
-2.6865    2.6865   -4.2984    2.6865
2.6865   -2.6865    4.2984   -2.6865
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Columns 5 through 6

2.6865   -4.2984
-2.6865    4.2984
4.2984   -6.8775
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2.6865   -4.2984
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Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN

Ke =

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218000           0           0
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-218000           0           0
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218000           0           0
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Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689   -5.5171   -4.1378
2.0689    1.0345   -2.7585   -2.0689
-5.5171   -2.7585    7.3561    5.5171
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Columns 5 through 6

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2.0689   -5.5171
1.0345   -2.7585
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Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689    5.5171   -4.1378
-2.0689    1.0345   -2.7585    2.0689
5.5171   -2.7585    7.3561   -5.5171
-4.1378    2.0689   -5.5171    4.1378
2.0689   -1.0345    2.7585   -2.0689
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Columns 5 through 6

2.0689   -5.5171
-1.0345    2.7585
2.7585   -7.3561
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1.0345   -2.7585
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Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689   -5.5171   -4.1378
-2.0689    1.0345    2.7585    2.0689
-5.5171    2.7585    7.3561    5.5171
-4.1378    2.0689    5.5171    4.1378
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Columns 5 through 6

2.0689    5.5171
-1.0345   -2.7585
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-2.0689   -5.5171
1.0345    2.7585
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Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689    5.5171   -4.1378
2.0689    1.0345    2.7585   -2.0689
5.5171    2.7585    7.3561   -5.5171
-4.1378   -2.0689   -5.5171    4.1378
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Columns 5 through 6

-2.0689   -5.5171
-1.0345   -2.7585
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2.0689    5.5171
1.0345    2.7585
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Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
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Columns 5 through 6

0         0
-0.1887    0.5033
0.5033   -1.3422
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0.1887   -0.5033
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Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
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Columns 5 through 6

0         0
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0.1887    0.5033
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Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887   -0.5033         0
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Columns 5 through 6

0         0
-0.1887    0.5033
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0.1887   -0.5033
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Ke =

1.0e+005 *

Columns 1 through 4

0         0         0         0
0    0.1887    0.5033         0
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0         0
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Ke =

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Columns 4 through 6

0           0           0
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Ke =

Columns 1 through 3

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Columns 4 through 6

0           0           0
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Ke =

Columns 1 through 3

218000           0           0
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Columns 4 through 6

-218000           0           0
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Ke =

Columns 1 through 3

218000           0           0
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Columns 4 through 6

-218000           0           0
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Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640    1.7192   -1.0745
2.3640    5.2007    3.7823   -2.3640
1.7192    3.7823    2.7508   -1.7192
-1.0745   -2.3640   -1.7192    1.0745
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Columns 5 through 6

-2.3640   -1.7192
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Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640    1.7192   -1.0745
-2.3640    5.2007   -3.7823    2.3640
1.7192   -3.7823    2.7508   -1.7192
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Columns 5 through 6

2.3640   -1.7192
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Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640   -1.7192   -1.0745
-2.3640    5.2007    3.7823    2.3640
-1.7192    3.7823    2.7508    1.7192
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Columns 5 through 6

2.3640    1.7192
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Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640   -1.7192   -1.0745
2.3640    5.2007   -3.7823   -2.3640
-1.7192   -3.7823    2.7508    1.7192
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Columns 5 through 6

-2.3640    1.7192
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Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640    3.7823   -5.2007
-2.3640    1.0745   -1.7192    2.3640
3.7823   -1.7192    2.7508   -3.7823
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Columns 5 through 6

2.3640   -3.7823
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Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640   -3.7823   -5.2007
2.3640    1.0745   -1.7192   -2.3640
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Columns 5 through 6

-2.3640    3.7823
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Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640    3.7823   -5.2007
2.3640    1.0745    1.7192   -2.3640
3.7823    1.7192    2.7508   -3.7823
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Columns 5 through 6

-2.3640   -3.7823
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Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640   -3.7823   -5.2007
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Columns 5 through 6

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Ke =

1.0e+004 *

Columns 1 through 4

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2.6865    2.6865    4.2984   -2.6865
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Ke =

1.0e+004 *

Columns 1 through 4

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Ke =

1.0e+004 *

Columns 1 through 4

2.6865    2.6865   -4.2984   -2.6865
2.6865    2.6865   -4.2984   -2.6865
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Columns 5 through 6

-2.6865    4.2984
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Ke =

NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
NaN   NaN   NaN   NaN   NaN   NaN
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Ke =

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Ke =

1.0e+004 *

Columns 1 through 4

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2.0689    1.0345   -2.7585   -2.0689
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Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689    5.5171   -4.1378
-2.0689    1.0345   -2.7585    2.0689
5.5171   -2.7585    7.3561   -5.5171
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1.0345   -2.7585
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Ke =

1.0e+004 *

Columns 1 through 4

4.1378   -2.0689   -5.5171   -4.1378
-2.0689    1.0345    2.7585    2.0689
-5.5171    2.7585    7.3561    5.5171
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Ke =

1.0e+004 *

Columns 1 through 4

4.1378    2.0689    5.5171   -4.1378
2.0689    1.0345    2.7585   -2.0689
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Ke =

1.0e+005 *

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0         0
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Ke =

1.0e+005 *

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Ke =

1.0e+005 *

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Ke =

1.0e+005 *

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Ke =

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Ke =

Columns 1 through 3

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Ke =

Columns 1 through 3

218000           0           0
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Columns 4 through 6

-218000           0           0
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Ke =

Columns 1 through 3

218000           0           0
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Columns 4 through 6

-218000           0           0
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Ke =

1.0e+004 *

Columns 1 through 4

1.0745    2.3640    1.7192   -1.0745
2.3640    5.2007    3.7823   -2.3640
1.7192    3.7823    2.7508   -1.7192
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Columns 5 through 6

-2.3640   -1.7192
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Ke =

1.0e+004 *

Columns 1 through 4

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1.7192   -3.7823    2.7508   -1.7192
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Columns 5 through 6

2.3640   -1.7192
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Ke =

1.0e+004 *

Columns 1 through 4

1.0745   -2.3640   -1.7192   -1.0745
-2.3640    5.2007    3.7823    2.3640
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Columns 5 through 6

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Ke =

1.0e+004 *

Columns 1 through 4

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2.3640    5.2007   -3.7823   -2.3640
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Columns 5 through 6

-2.3640    1.7192
-5.2007    3.7823
3.7823   -2.7508
2.3640   -1.7192
5.2007   -3.7823
-3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640    3.7823   -5.2007
-2.3640    1.0745   -1.7192    2.3640
3.7823   -1.7192    2.7508   -3.7823
-5.2007    2.3640   -3.7823    5.2007
2.3640   -1.0745    1.7192   -2.3640
-3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640   -3.7823
-1.0745    1.7192
1.7192   -2.7508
-2.3640    3.7823
1.0745   -1.7192
-1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640   -3.7823   -5.2007
2.3640    1.0745   -1.7192   -2.3640
-3.7823   -1.7192    2.7508    3.7823
-5.2007   -2.3640    3.7823    5.2007
-2.3640   -1.0745    1.7192    2.3640
3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640    3.7823
-1.0745    1.7192
1.7192   -2.7508
2.3640   -3.7823
1.0745   -1.7192
-1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007    2.3640    3.7823   -5.2007
2.3640    1.0745    1.7192   -2.3640
3.7823    1.7192    2.7508   -3.7823
-5.2007   -2.3640   -3.7823    5.2007
-2.3640   -1.0745   -1.7192    2.3640
-3.7823   -1.7192   -2.7508    3.7823

Columns 5 through 6

-2.3640   -3.7823
-1.0745   -1.7192
-1.7192   -2.7508
2.3640    3.7823
1.0745    1.7192
1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   -2.3640   -3.7823   -5.2007
-2.3640    1.0745    1.7192    2.3640
-3.7823    1.7192    2.7508    3.7823
-5.2007    2.3640    3.7823    5.2007
2.3640   -1.0745   -1.7192   -2.3640
3.7823   -1.7192   -2.7508   -3.7823

Columns 5 through 6

2.3640    3.7823
-1.0745   -1.7192
-1.7192   -2.7508
-2.3640   -3.7823
1.0745    1.7192
1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

2.6865    2.6865    4.2984   -2.6865
2.6865    2.6865    4.2984   -2.6865
4.2984    4.2984    6.8775   -4.2984
-2.6865   -2.6865   -4.2984    2.6865
-2.6865   -2.6865   -4.2984    2.6865
-4.2984   -4.2984   -6.8775    4.2984

Columns 5 through 6

-2.6865   -4.2984
-2.6865   -4.2984
-4.2984   -6.8775
2.6865    4.2984
2.6865    4.2984
4.2984    6.8775

Ke =

1.0e+004 *

Columns 1 through 4

2.6865   -2.6865    4.2984   -2.6865
-2.6865    2.6865   -4.2984    2.6865
4.2984   -4.2984    6.8775   -4.2984
-2.6865    2.6865   -4.2984    2.6865
2.6865   -2.6865    4.2984   -2.6865
-4.2984    4.2984   -6.8775    4.2984

Columns 5 through 6

2.6865   -4.2984
-2.6865    4.2984
4.2984   -6.8775
-2.6865    4.2984
2.6865   -4.2984
-4.2984    6.8775

Ke =

1.0e+004 *

Columns 1 through 4

2.6865    2.6865   -4.2984   -2.6865
2.6865    2.6865   -4.2984   -2.6865
-4.2984   -4.2984    6.8775    4.2984
-2.6865   -2.6865    4.2984    2.6865
-2.6865   -2.6865    4.2984    2.6865
4.2984    4.2984   -6.8775   -4.2984

Columns 5 through 6

-2.6865    4.2984
-2.6865    4.2984
4.2984   -6.8775
2.6865   -4.2984
2.6865   -4.2984
-4.2984    6.8775

Ke =

1.0e+004 *

Columns 1 through 4

2.6865   -2.6865   -4.2984   -2.6865
-2.6865    2.6865    4.2984    2.6865
-4.2984    4.2984    6.8775    4.2984
-2.6865    2.6865    4.2984    2.6865
2.6865   -2.6865   -4.2984   -2.6865
4.2984   -4.2984   -6.8775   -4.2984

Columns 5 through 6

2.6865    4.2984
-2.6865   -4.2984
-4.2984   -6.8775
-2.6865   -4.2984
2.6865    4.2984
4.2984    6.8775


## Problem 5

On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.


### Find

Vibration analysis of 3-D truss system in R6.4

### Solution


clear
clc

E=3*10^7;  A=0.0218;
rho= 7.3*10^(-4);

Edof=[1 1 2 3 4 5 6;
2 1 2 3 10 11 12 ;
3 4 5 6 7 8 9;
4 1 2 3 13 14 15;
5 4 5 6 16 17 18;
6 4 5 6 10 11 12;
7 4 5 6 13 14 15;
8 1 2 3 7 8 9;
9 1 2 3 16 17 18;
10 7 8 9 16 17 18;
11 10 11 12 13 14 15;
12 7 8 9 10 11 12;
13 13 14 15 16 17 18;
14 7 8 9 28 29 30;
15 16 17 18 19 20 21;
16 10 11 12 25 26 27;
17 13 14 15 22 23 24;
18 10 11 12 19 20 21;
19 7 8 9 22 23 24;
20 13 14 15 28 29 30;
21 16 17 18 25 26 27;
22 16 17 18 28 29 30;
23 7 8 9 19 20 21;
24 10 11 12 22 23 24;
25 13 14 15 25 26 27];

coord=[-1.5   0   8;
1.5    0   8;
-1.5  1.5  4;
1.5   1.5  4;
1.5  -1.5  4;
-1.5 -1.5  4;
-4     4   0;
4     4   0;
4    -4   0;
-4    -4   0];

ex=zeros(25,2);
ey=zeros(25,2);
ez=zeros(25,2);
for i=1:25
ex(i,1)=coord((Edof(i,2)+2)/3,1);
ex(i,2)=coord((Edof(i,5)+2)/3,1);
ey(i,1)=coord((Edof(i,3)+1)/3,2);
ey(i,2)=coord((Edof(i,6)+1)/3,2);
ez(i,1)=coord(Edof(i,4)/3,3);
ez(i,2)=coord(Edof(i,7)/3,3);
end

K=zeros(75,75);
M=zeros(75);
for i=1:25

dx=ex(i,2)-ex(i,1) ;
dy= ey(i,2)-ey(i,1);
dz=ez(i,2)-ez(i,1) ;

L=sqrt(dx^2+dy^2+dz^2);
Kle=E*A/L*[1 -1;
-1  1];
l=dx/L;
m=dy/L;
n=dz/L;
G=[l m n 0 0 0;
0 0 0 l m n];
mass=L*A*rho;
me=[mass/2 0 0 0 0 0;
0 mass/2 0 0 0 0;
0 0 mass/2 0 0 0;
0 0 0 mass/2 0 0;
0 0 0 0 mass/2 0;
0 0 0 0 0 mass/2];
Ke=G'*Kle*G;
S=Edof(i,2:7);
K(S,S)=K(S,S)+Ke;
M(S,S)=M(S,S)+me;

end
nd=size(K,1);
fdof=[1:nd]';
bc=[25 26 22 24 19 21 28 30 ]';
fdof(bc(:))=[];
[X,D]=eig(K(fdof,fdof),M(fdof,fdof));
nfdof=size(X,1);
eigenval=diag(D);
eigenvec=zeros(nd,nfdof);
eigenvec(fdof,:)=X;
%top
for kk=1:3
eigenvalx=eigenval(kk);
eigenvecx=eigenvec(:,kk);
w=sqrt(eigenvalx);
T=2*pi/w;
dt=T/100;
t=0:dt:T;
figure(kk)

if kk==1;
filename = 'mode1_top.gif';
elseif kk==2;
filename = 'mode2_top.gif';
elseif kk==3;
filename = 'mode3_top.gif';
end

for jj = 1:100
tt=t(jj);
d=eigenvecx*sin(w*tt);
d=d';
rr=Edof(:,2:7);
ed=zeros(25,6);
for i=1:25;
ed(i,1:6)=d(rr(i,:));
end
xd=(ex+ed(:,[1 4]))';
yd=(ey+ed(:,[2 5]))';
zd=(ez+ed(:,[3 6]))';
s1=['-' , 'k'];
axis manual
plot(xd,zd,s1)
set(gca, 'ylim', [-12 12], 'xlim', [-12 12]);
drawnow
frame = getframe(1);
im = frame2im(frame);
[imind,cm] = rgb2ind(im,256);
if jj == 1;
imwrite(imind,cm,filename,'gif', 'Loopcount',inf);
else
imwrite(imind,cm,filename,'gif','WriteMode','append');
end
end
end
%side
for kk=1:3
eigenvalx=eigenval(kk);
eigenvecx=eigenvec(:,kk)
w=sqrt(eigenvalx)
T=2*pi/w;
dt=T/100
t=0:dt:T;
figure(kk)

if kk==1;
filename = 'mode1_side.gif'
elseif kk==2;
filename = 'mode2_side.gif'
elseif kk==3;
filename = 'mode3_side.gif'
end

for jj = 1:100
tt=t(jj);
d=eigenvecx*sin(w*tt);
d=d';
rr=Edof(:,2:7);
ed=zeros(25,6);
for i=1:25;
ed(i,1:6)=d(rr(i,:));
end
xd=(ex+ed(:,[1 4]))';
yd=(ey+ed(:,[2 5]))';
zd=(ez+ed(:,[3 6]))';
s1=['-' , 'k'];
axis manual
plot(xd,yd,s1)
set(gca, 'ylim', [-12 12], 'xlim', [-12 12]);
drawnow
frame = getframe(1);
im = frame2im(frame);
[imind,cm] = rgb2ind(im,256);
if jj == 1;
imwrite(imind,cm,filename,'gif', 'Loopcount',inf);
else
imwrite(imind,cm,filename,'gif','WriteMode','append');
end
end
end


Top and Side view for Mode 1:

Top and Side view for Mode 2:

Top and Side view for Mode 3:

## Contributing Team Members

Problem Assignments
Problem # Solved & Typed by Reviewed by
1 Zeyn Kermani All
2 Matthew Gidel All
3 Joshua Plicque All
4 Brandon Wright,Spencer Herran All
5 Kelvin Li,Matthew Gidel All

On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.