On applying polyharmonic radial basis functions to solve 3D uncoupled anisotropic thermoelasticity problems using Boundary Element and Dual Reciprocity Method

Abstract

This paper presents the uncoupled anisotropic thermoelasticity formulation for Boundary Element using the Dual Reciprocity Method. The proposed formulation demands two interpolation functions, one for the particular solution of the elastic problem and another to interpolate the derivatives of the thermal field. For the last one, the shape parameter of multiquadric Radial Basis Functions (RBF) was demonstrated to be a problem to be solved. Some polyharmonic RBFs were tested and a modified function was proposed. Singularity at derivatives of some functions made them impossible to be used and some of them demonstrated great sensibility to saturation. The use of internal points was mandatory under temperature fields irregularly distributed. Few polyharmonic functions were suitable to be used for thermoelasticity and low order functions presented reliable solutions, with the proposed modified RBF presenting slightly better performance over the previously used function.