The meshless local technique is employed to simulate potential problems involving material anisotropy and also plane elastostatic equations of anisotropic functionally graded materials (PEE-AFGM). We utilize direct meshless local Petrov Galerkin (DMLPG) technique to discrete the spatial directions. The DMLPG5 (based on weak form) is applied to solve potential problems involving material anisotropy and the DMLPG2 (based on strong form) is employed to simulate PEE-AFGM. The coefficients of the anisotropic conductivity require the gradient term to be modified accordingly. The grading function can be any general function that varies smoothly from point to point in the material. The developed procedures are tested on various examples on non-rectangular domains to check their accuracy.

采用无网格局部技术来模拟涉及材料各向异性以及各向异性功能梯度材料（PEE-AFGM）的平面弹性方程的潜在问题。我们利用直接无网格局部Petrov Galerkin（DMLPG）技术来离散空间方向。DMLPG5（基于弱形式）用于解决涉及材料各向异性的潜在问题，而DMLPG2（基于强形式）用于模拟PEE-AFGM。各向异性电导率的系数要求对梯度项进行相应的修改。渐变功能可以是在材质中随点平滑变化的任何常规功能。在非矩形区域的各种示例上测试了开发的过程，以检查其准确性。