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.

在这项研究中，基本解法（MFS）是一种边界型无网格法，用于解决二维静态各向异性热弹性问题。由于MFS的半分析性质，可以通过此方法获得非常准确的解决方案。该问题的解决方案被分解为同类解决方案和特定解决方案。均质解用各向异性弹性静力学问题的基本解表示。特定的解决方案对应于问题领域中温度变化的影响。对于域中温度变化呈二次分布的情况，以显式形式导出特定解决方案。对于具有任意温度变化分布的情况，热负荷通过径向基函数（RBF）近似，其特定解决方案通过解析得出。给出了在平面应力和平面应变条件下的简单连接域和多重连接域中的三个数值示例，以验证所提出方法的准确性。研究了某些参数（例如源点的数量和源点的位置参数的大小）对结果的影响。从数值结果可以看出，对于温度变化分布非常复杂的问题，所提出的MFS可以获得非常准确的结果。