为了解决具有凹凸边界形状的平面非定常拟静态热力耦合问题，采用无网格伽辽金算法(EFG)进行求解，使用移动最小二乘法构造形函数，使用拉格朗日乘子法处理本质边界条件（第一类边界条件），通过引入Voronoi邻接准则和后验误差式，对后续结果进行自适应优化；继而构建了一种新的适用于非定常拟静态热力耦合问题的无网格伽辽金（EFG）法自适应计算模型；为了验证计算模型的可行性，分别计算了在二维混合边界条件下光滑与凹凸边界形状平面的温度场以及位移场的分布，并与有限单元法的计算结果进行了对比，表征了有限单元法和无网格法计算结果的差异，验证了非定常拟静态热力耦合问题的无网格伽辽金（EFG）法计算模型的有效性和精确性。

In order to solve the plane unsteady and quasi-static coupled thermoelasticity problems with concave convex boundary shape, the element free Galerkin method (EFG) is used to solve the problem, the Moving least square method（MLS） is used to construct the shape function, the Lagrange multiplier method is used to deal with the essential boundary conditions (the first kind of boundary conditions), the Voronoi adjacency criterion and the posteriori error formula are introduced to adaptively optimize the subsequent results; A new EFG adaptive model for unsteady quasi-static and coupled thermoelasticity problems is constructed. The temperature field and displacement field distribution in the planes with smooth and concave convex boundary shape are calculated under two-dimensional mixed boundary conditions, respectively. And the results are compared with those of finite element method. The difference between the results of finite element method and meshless method is characterized, and the effectiveness and accuracy of EFG for unsteady quasi-static thermoelasticity coupled problem are verified

国家自然科学基金项目（面上项目，重点项目，重大项目）