A Combined Laplace Transform and Boundary Element Method for Unsteady Laplace Problems of Several Classes of Anisotropic Functionally Graded Materials

In this paper a combined Laplace transform and boundary element method is used to find numerical solutions to unsteady problems of anisotropic functionally graded materials governed by a Laplace type equation. A mathematical transformation is used to transform the variable coefficients equation to a constant coefficients equation from which a boundary-only integral equation is obtained. In addition, the analysis also results in several classes of inhomogeneity functions for the functionally graded materials. Some examples are considered to show the validity of the analysis and accuracy of the numerical solutions. A verification for the effect of the anisotropy and inhomogeneity of the material on the solutions is also demonstrated.