Elementary applications of MATHEMATICA to the solution of elasticity problems by the finite element method

Abstract

The computer algebra system MATHEMATICA is used for the SAN (semi-analytical/numerical) solution of two simple elasticity problems, having been reduced to systems of linear algebraic equations by the finite element method. In both cases, one parameter was left in symbolic form and Taylor series expansions with respect to this parameter (either a material constant or a geometric parameter) were used in the SAN results. The Gauss-Seidel iterative method for systems of linear equations and its SOR variant were used for the solution of the systems of linear equations always in the SAN environment offered by MATHEMATICA. The SAN results were compared with the corresponding numerical results and they were found to be equally acceptable. The present approach, which can be generalized in a variety of ways, offers the advantage (over purely numerical techniques) that it permits the incorporation of symbolic parameters into the results of the finite element method.