A Meshless Local Boundary Integral Equation Approach Applied to Functionally Graded Viscoelastic Solid Polymers

The Functionally Graded Materials (FGMs) are the special composite materials usually made from both ceramics and metals. A few models for functionally graded viscoelastic materials are presented and discussed in the literature. The present study introduces a new meshless method based on the local Petrov- Galerkin approach for the solution of quasistatic problems in two-dimensional functionally graded viscoelastic solid polymers. A unit step function is used as the test functions in the local weak form. It is leading to local boundary integral equations involving only a domain integral. The correspondence principle is applied to such nonhomogenous linear viscoelastic solids where the relaxation moduli are separable in space and time variables. The local boundary integral equations are formulated for Laplace transformed viscoelastic problems. An inversion method is applied to obtain the final time-dependent solutions. The local integral equations are nonsingular and take a very simple form. An effective example, as application, involving an exponentially graded viscoelastic material, is illustrated in this paper.

Keywords:

functionally graded viscoelastic polymers , local Petrov-Galerkin approach , boundary integral equations , weak form