Nonlinear finite elements/Homework 6/Solutions/Problem 1/Part 8
Problem 1: Part 8 
Consider the curved composite beam shown in Figure 12.
Assume that the beam has been shaped into an arc of a circle. The material of the beam is a transversely isotropic fiber composite material with the fibers running along the length of the beam. The rate constitutive relation of the material is given by
The problem becomes easier to solve if we consider numerical values of the parameters. Let the local nodes numbers of element be for node , and for node .
Let us assume that the beam is divided into six equal sectors. Then,
Let and . Since the blue point is midway between the two, .
Also, let the components of the stiffness matrix of the composite be
Let the velocities for nodes and of the element be
The Maple code for these initializations is shown below
> with(linalg): > # > # Input geometry > # > theta:= evalf(Pi/4): > theta1 := evalf(theta + Pi/12): > theta2 := evalf(theta - Pi/12): > r1:= 1; r2 := 1.2; r:= (r1+r2)/2; > # > # Input material properties > # > C11 := 10; C33:= 100; C12:= 6; C13 := 60; C44 := 30; > CC := (C11-C12)/2; > # > # Input velocities > # > vx1 := 1; vy1 := 2; w1 := 1; > vx2 := 2; vy2 := 1; w2 := 1; > v1master := linalg[matrix](3,1,[vx1,vy1,w1]); > v2master := linalg[matrix](3,1,[vx2,vy2,w2]);