Elastic Torsion of Bars with “Pound” and “Yen” Cross Sections Using Large Singular Finite Element Method

Abstract

Aims: Solving Dirichlet’s problem through large singular finite elements method for the Poisson’s equation. Study design: Large Singular Finite Elements Method (LSFEM). Place and Duration of Study: Sample: Department of Physics, UFR-SEA, University of Ouagadougou, Burkina Faso, between September 2010 and July 2012. Methodology: There are 3 steps for LSFE Method; After the decomposition of the domain in subdomains, we resolve auxiliary problems and connect auxiliary solutions, using MATLAB software. Results: For each of both membranes, the minimum global error is 1.3x10-12. It is obtained at the twelfth approximation when coefficients aki  are maintained as a whole. This suggests that the distorted u of the membrane can be determined with 13 or 14 significant digits, while its derivatives     and  may be calculated with 11 or 12 significant digits. These results are compared with those obtained through finite elements method. Both methods provide results that align quite well everywhere except near the singularities with significant differences.