无网格伽辽金法在静态力学中的应用

The application of Element-Free Galerkin Method to the static mechanics

无网格伽辽金法(EFGM)作为一种新兴的数值算法,部分地摆脱了网格的束缚,表现出计算精度高、收敛快、数值稳定等一系列突出优点,同时也表现出了一些不足。利用拉格朗日乘子法施加本质边界条件,对静态力学中的梁在各种不同受力情况下的变形问题进行详细计算,并对计算结果进行误差分析。结果表明,在许多量的计算中,该方法的计算结果与理论解还是相当吻合的,同时也存在着对某些量的计算精度还不是很精确的缺点。

As a new numerical method developed recently,the Element-Free Galerkin Method（EFGM） has a lot of advantages,which include eliminate part of the mesh,high precision,stabile and post-processing convenient and so on.However,the Element-Free Galerkin Method also has some insufficient.Some problems of the static beam under different pressure are computed and analyzed by employing Lagrange multiply method to satisfy essential boundary conditions.The numerical example shows that the obtained results are very similar with the exact results in some area,meanwhile,in other area is not very precise,that should be studied further.