The use of dual reciprocity boundary element method in coupled thermoviscoelasticity

A boundary element formulation is presented in a unified form for the analysis of thermoviscoelasticity problems. The formulation contains the thermoelastic material as a special case. The boundary-only nature of boundary element method is retained through the use of particular integral method; where the particular solutions are evaluated with the aid of dual reciprocity approximation. The proposed formulation can be used in both coupled and uncoupled thermoviscoelasticity analyses, and it permits performing the analysis in terms of fundamental solutions of viscoelastodynamics and diffusion (thermal) equation, and eliminates the need for using the complicated fundamental solutions of coupled thermoviscoelasticity. The formulation is performed in Fourier space where any viscoelastic model can be simulated via the correspondence principle. The determination of the response in time space requires the inversion which can be carried out conveniently by using the fast Fourier transform algorithm. For assessment, some sample problems, both uncoupled and coupled, are considered and whenever possible comparisons are given with the exact data. It is found that the formulation developed in the study, even with the simplest base function proposed in literature, may be used reliably in thermoviscoelasticity analysis, at least, for the problems with finite solution domains

Numerical analysis for nonlinear heat transfer problems using DRM

The boundary element method (BEM) proves to be a powerful alternative numerical method for solving non-linear diffusion problems. In the BEM the mesh is generated only on the surface of a 3D body or on the contour if the domain is 2D. In order to impose body forces to the problem a technique called as Dual Reciprocity Method (DRM) was introduced. The DRM allows to transform the domain integrals into the boundary equivalent integrals by expanding the inhomogeneous terms into a set of global approximating basis functions. In this work a numerical routine based on BEM is implemented for solving a non-linear problem and the non-homogeneous terms were dealt by using the DRM. The routine is validated by using a benchmark of a 2D cube model submitted to a thermal load increment