Stepwise linear regression particular integrals for uncoupled thermoelasticity with boundary elements

This paper presents a simple technique for the efficient treatment of non-uniform body forces in boundary elements without the need for domain discretization and additional surface integral evaluations. The distribution of the non-uniform forces in the domain is described using regression polynomials. Particular integrals corresponding to these polynomials are developed for the solution of the non-homogeneous differential equations of elasticity. Two-dimensional and axisymmetric boundary element results for steady state and transient thermoelastic deformations are obtained using this formulation. Regression polynomials based on only the boundary points provide good results. Improved results are obtained by including internal points in the regression analysis. The method allows the use of low order polynomials to model a general distribution of thermal effects in the domain. Numerical data are given to provide comparisons of low order versus high order regression polynomials, and boundary only data versus combined boundary and domain data based regression polynomials.