User:Eml5526.s11.team01.roark/Mtg29

Mtg 29: Fri, 4 Mar 11

Page 29-1

Ex: $\displaystyle n=4,{{y}_{1}}=1,{{y}_{2}}=2,{{y}_{3}}=3,{{y}_{4}}=4$

$\displaystyle {{L}_{\underbrace{1}_{j},\underbrace{4}_{n}}}\left( y \right)=\frac{\left( y-{{y}_{2}} \right)\left( y-{{y}_{3}} \right)\left( y-{{y}_{4}} \right)}{\left( {{y}_{1}}-{{y}_{2}} \right)\left( {{y}_{1}}-{{y}_{3}} \right)\left( {{y}_{1}}-{{y}_{4}} \right)}=\frac{\left( y-2 \right)\left( y-3 \right)\left( y-4 \right)}{\left( 1-2 \right)\left( 1-3 \right)\left( 1-4 \right)}$

(1)

Page 29-2

Ex: 2-D LIBF

$\displaystyle {{N}_{I}}\left( x,y \right)={{L}_{i,m}}\left( x \right)\cdot {{L}_{j,n}}\left( y \right)\,\,\,,\,\,\,I=i+\left( j-1 \right)m$

(2)

Page 29-4

A different perspective:

Important prop of LIBF: c.f. FB, p.80, (4.7) 1-D:

$\displaystyle {{L}_{i,m}}\left( {{x}_{j}} \right)={{\delta }_{ij}}$

(1)

2-D:

$\displaystyle {{N}_{I}}\left( {{\mathbf x}_{J}} \right)={{\delta }_{IJ}}$

(2)

(3-D) $\displaystyle {{x}_{J}}=\left( x_{J}^{1},x_{J}^{2} \right)=\left( {{x}_{J}},{{y}_{j}} \right)$

Page 29-5

 plot[{{(x-1)(x-2)(x-4)}/{(3-1)(3-2)(3-4)}}*{{(y-2)(y-3)(t-4)}/{(1-2)(1-3)(1-4)}}],1<=x<=4, 1<=y<=4

Page 29-6

HW5.3:

Similar to HW 5.1, but using LIBF with uniform discretization (equidistant nodes. m=4.6.8,…

1. Explain how LIBF are used as a CBS
2. Plot all LIBF used.
3. Use matlab quad, WA,… to int.
4. Plot $\displaystyle u_{m}^{h}$ vs $\displaystyle u$, $\displaystyle u_{m}^{h}\left( 0.5 \right)-u\left( 0.5 \right)$vs. m

End HW 5.3

HW 5.4:

Similar to HW 5.2, but using LIBF with uniform discretization (equidistant nodes. m=4.6.8,…

Same tasks as in HW 5.3

End HW 5.4

Page 29-7

HW5.5:

Continuation of HW 4.7 on Calculix

1. For the disk problem, extract: Node info: node numbers and coordinates, and Element info: element numbers and element nodes.
2. Generate 3 meshes of same disk with triangular elements (increase number of elements)
3. Install ccx, run examples, write report for “dummies” (explain commands, screenshots, …)

End HW 5.5