The method of fundamental solutions for anisotropic thermoelastic problems

Abstract

In this study, the method of fundamental solutions (MFS), which is a boundary-type meshfree method, is applied for solving two-dimensional stationary anisotropic thermoelastic problems. Because of the semi-analytic nature of the MFS, very accurate solutions can be obtained by this method. The solution of the problem is decomposed into homogeneous and particular solutions. The homogeneous solution is expressed in terms of the fundamental solutions of the anisotropic elastostatic problem. The particular solution corresponds to the effects of the temperature change in the domain of the problem. For cases with a quadratic distribution of the temperature change in the domain, the particular solution is derived in an explicit form. For cases with an arbitrary temperature change distribution, the thermal load is approximated by radial basis functions (RBFs), particular solutions of which are derived analytically. Three numerical examples in simply- and multiply-connected domains under plane stress and plane strain conditions are presented to verify the accuracy of the proposed method. The effects of some parameters, such as the number of source points and the magnitude of the location parameter of source points on the results are investigated. From the numerical results, it is observed that very accurate results can be obtained by the proposed MFS in problems with very complicated temperature change distribution. The numerical convergence tests performed in this study shows that the proposed MFS with a small number of source points can results in solutions that are comparable with the FEM solutions obtained using a large number of nodes.