Finite Elements in Solid Mechanics I

Project

Consider heat conduction in a 2-dimensional plate with geometry given in Fig.1. The isotropic thermal conductivity of the plate is k=50 W/(m oC), the heat input per area is W/m3 , the boundaries and are insulated (h=0 W/m2 ), and the boundaries and are prescribed with zero temperature (u=0 oC).

The analytical solution of this problem is

(1) Obtain finite element solutions using 8x8, 16x16, and 32x32 4-node elements, and compare the finite element solutions u h with the analytical solution u along the line x=0.5 in a plot.

(2) Compare the finite element solutions obtained by using the 3 discretizations with the analytical solution along the line x=0.5 in a plot.

(3) Plot the errors of finite element solutions vs element dimensions “h” in a log-log plot and obtain the rate of convergence of this error measure.

(4) Discuss how the fiunite element solution errors are reduced as the model is refined, and how the numerical rate of convergence compares with the theoretical rate of convergence.

The final report should contain problem statement, finite element formulation, numerical results, and discussions. A copy of your program should be attached.