Chris Bickford
Introduction to Finite Elements
HW #5; Problem 3
MAPLE:
Maple software was used to solve for the exact solution. The value at u(0.2, 0) is 1 and
the value at u(0.2, 0.15) is 0 for the exact solution. The value at u(0.3, 0.15) is 0.95 for
the exact solution. See attached maple sheet for more details.
ABAQUS FEA CODE:
ABAQUS 6.14 software was used to perform finite element analysis (FEA) to obtain an
approximate solution for problem (2). A 2-dimensional transient heat transfer analysis
was performed assuming no boundary conditions on the top (x , 0.5) and bottom (x, 0.5) edges, which effectively makes the problem one-dimensional. The temperature
over the domain is close to zero after 1 second, which is approaching the exact solution.
Figure 2 shows a time history of the value at x = 0.2, which starts at one and begins to
approach zero at about t = 0.40s, which is later than the exact solution (t=0.15s).
Figure 1 FEM Mesh Density
Figure 2 Time-History of the Value at x = 0.2: Quadratic Element Type
Figure 3 Time-History of the Value at x = 0.2: Exact Solution