A boundary integral investigation for unsteady modified Helmholtz problems of some other classes of anisotropic functionally graded materials

Abstract

Numerical solutions for a class of unsteady modified Helmholtz problems of anisotropic functionally graded materials are sought. The governing equation which is a variable coefficients equation is transformed to a constant coefficients equation. The time variable is transformed using the Laplace transform. The resulted partial differential equation of constant coefficients and time free variable is then converted to a boundary integral equation, from which boundary element solutions can be obtained. Some examples are considered to verify the accuracy, convergence and consistency of the numerical solutions. The results show that the numerical solutions are accurate, convergent and consistent.