Problem 1 AE4132 - Finite Element Analysis Spring 2022 Homework 4: 1D Bar Elements in 2D Space Due Friday, March 18th 2022 Write a finite element program in Phython to solve for 2-dimensional trusses....

Problem 1

AE4132 - Finite Element Analysis

Spring 2022

Homework 4: 1D Bar Elements in 2D Space

Due Friday, March 18th 2022

1. 
   

   Write a finite element program in Phython to solve for 2-dimensional trusses. You can use 1D elements as discussed in class. The program should be able to read an input file with the following format:
   

   
   

   nnodes
   x1 y1 rx1 ry1 fx1 fy1
   x2 y2 rx2 ry2 fx2 fy2
   .
   .
   .
   x nnodes y nnodes rx nnodes ry nnodes fx nnodes fy nnodes nels
   n11 n21 E1 A1
   n12 n22 E2 A2
   .
   .
   .
   n1 nels n2 nels E nels A nels
   

   
   

   Where nnodes denotes the total number of nodes in the structure, (x i, y i) the coordinates of node i, (rx i, ry i) the constraints in the x and y directions for node i (1 means constrained, 0 free to move), and (fx i, fy i) the x and y component of the force applied at node i. Also, nels represents the number of elements in the structure, (n1 i, n2 i) the first and second node of element i, and E i and A i the corresponding Young’s modulus and cross-sectional area. Note that the length of each element has to be computed based on its connectivity. That is, for a given element, you can get n1 and n2, and with them the coordinates of the corresponding nodes.
   

   
   


2. 
   

   Test your program on a simple structure you can check by hand, e.g., a simply supported triangle composed of three bars like the one discussed in class.
   

   
   


3. 
   

   Once the program is written and tested, write the input files for the structures shown in Figure 1 and solve for all nodal displacements. All bars have identical cross-sectional area A = 0.1cm2 and Young’s modulus E = 70 GPa.
   

   
   


4. 
   

   Plot the deformed structure for each case, coloring the bars according to the stress they are subject to. Magnify displacements if needed to facilitate visualization.
   

   
   


5. 
   

   Compute the reaction forces.
   

   
   

AE4132: Finite Element Analysis - Spring 2022, Homework 4

2

4321

1.5m

56789

30°

P=800N
2m 2m 2m 2m

4321

Figure 1: Structures for problem 1.

1.5m