AE4132 - Finite Element AnalysisSpring 2022
Homework 5: Rectangular Elements for Stress Analysis
Due Friday, April 8th 2022
1 Problem 1
Write a finite element program that utilizes rectangular elements as developed in class. The program should be
able to read input files with the format described in Appendix 1. Five meshes, representing different levels of
discretization of a clamped beam loaded axially are provided.
1. For each mesh, please provide:
(a) Plots showing deformed configuration (amplified if necessary for visualization purposes).
(b) Contour plots of all components of strain and stress over the domain.
2. Also, provide the following convergence plots:
(a) Maximum nodal displacement over the domain.
(b) Maximum von Mises stress over the domain.
(c) Strain energy of the entire beam.
3. Discuss your findings regarding convergence.
NOTES:
•Do not worry about units, assume all units are provided consistently.
•For convergence plots, depict the total number of elements on the x-axis and the other variable of interest
on the y-axis. Also, explore different scales for the axis to get more insights (e.g., log-log, semi-log, etc.)
Appendix 1: Input file format
nnodes
x 1 y 1 rx 1 ry 1 fx 1 fy 1
x 2 y 2 rx 2 ry 2 fx 2 fy 2
.
.
.
x nnodes y nnodes rx nnodes ry nnodes fx nnodes fy nnodes
nels
n1 1 n2 1 n3 1 n4 1 E 1 nu 1 h 1
n1 2 n2 2 n3 2 n4 2 E 2 nu 2 h 2
.
.
.
n1 nels n2 nels n3 nels n4 nels E nels nu nels h 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, n3 i, n4 i) the nodes of element i in counterclockwise direction, and
E i, nu i, and h i the corresponding Young’s modulus, Poisson ratio, and thickness.