A Boundary Element Formulation for the Heterogeneous Functionally Graded Viscoelastic Structures

Abstract

Structural analysis of the heterogeneous viscoelastic materials is among the most important subjects in the engineering design stages. Several attempts have been performed so far for employing the integral equation approach to heterogeneous viscoelastic structures. In the present research, employing two viscoelastic constitutive equations and a weighted residual technique, a simple but effective boundary element formulation is implemented for heterogeneous Kelvin–Voigt and Boltzmann viscoelastic solid models. The Boltzmann model provides proper behavior predictions for realistic structures manifest viscoelastic natures. Present formulation needs only fundamental solution of the heterogeneous elastostatic problem with materials whose properties are prescribed as explicit functions of time. Heterogeneous exponentially graded materials and quasistatic time variations are considered in the present formulation. Present approach does not require using the relaxation functions and mathematical transformations and is capable of solving quasistatic viscoelastic problems with arbitrary load–time dependencies and boundary conditions. Some numerical examples are provided to verify the proposed boundary element approach.