Symbolic Algebra Approach to Composite Materials Analysis

Abstract

Application of symbolic algebra to the analysis of composite materials is presented in this paper. The classical Galerkin method is implemented using symbolic algebra software without which tedious and error-prone calculation is unavoidable. Symbolic algebra can generate transcendental functions (or polynomials) that can satisfy given boundary conditions for a given arbitrary geometry automatically which can be used in the Galerkin method as trial functions. Symbolic algebra can also generate the stiffness and mass matrix elements that require analytical differentiation, integration and expansion of the trial functions. The proposed method has successfully been applied to two typical problems in the analysis composite materials: 1) a composite plate with free edge boundary conditions and 2) a finite elastic body that contains spherical inhomogeneities.