Homework 3
AE420/ME471/CSE453 – Introduction to the finite element
method
Date issued: 6-26-24
This is an optional homework for students doing 3 credit hours (we will
discount the lowest HW score if you choose to this). For students doing 4
credit hours, this HW is compulsory.
Upload to Canvas your printed code and output of the code by
11.59 pm 7-5-24
Topic 3: Finite element formulation and analysis for 2D Thermal Problem
Consider the following finite element mesh with the boundary conditions indicated (2 sides
adiabatic, 2 sides with uniform temperatures specified). Write a finite element code in ANY
language that you wish (MATLAB, fortran, C, etc.) to find the temperature distribution at all the
nodes. Note the following:
(a) The specified input to the code should be the nodal temperatures at nodes 1-3 and 11-14,
along with the heat flux q = 0 at nodes 4,7,8,10 (nodes 1,3,11,14 are corner nodes that still
have to maintain the specified temperatures so the heat flux cannot be 0).
(b) You can directly use the expressions for the local stiffness matrix and local load vector of
a generic element, but you need to write a code to populate each local stiffness matrix and
local load vector, and in turn to populate the global stiffness matrix and global load vector.
(c) Assume Q = 0, and thermal conductivities kxx = kyy = 45 W/mK.
(d) For ways to start the coding, I recommend looking in the notes on the chapter on 1D FEM
where example codes are provided.
(e) The output should be the nodal temperatures.
T = 25°C
T = 200°C
1
2
3
4
5
6
8
10
13
12
1
2
3
4
5
6
8
9
14
11
14
13
12
15
11
7
10
7
9
3m
2m
