Non-Singular Method of Fundamental Solutions for Two-dimensional Thermoelasticity

Abstract

A framework for simulation of thermomechanical processing of microstructures by the method of fundamental solutions, free of artificial boundary, is shown. The formulation of the method for two-dimensional thermal and mechanical models is presented. In particular, the formulation for elastic and thermo-elastic problems is discussed. In the thermal and mechanical models, the concentrated point sources are replaced by the distributed sources over the sphere around the singularity to regularize the singularities. The balance of heat fluxes and forces is used to calculate some of the otherwise singular diagonal coefficients. This procedure enables also to solve a broad spectra of thermomechanical problems. The novel boundary meshless method has been assessed by comparison with the method of fundamental solutions, and analytical solution. The method is easy to code, accurate, and efficient.