基于转换矩阵的FEM/MLPG耦合算法

FEM/MLPG coupling algorithm using transform matrices

首次基于有限元的转换矩阵(TMF)和无网格的转换矩阵(TMM),提出有限单元法(FEM)和无网格局部彼得罗夫-伽辽金法(MLPG)的耦合算法。编制了相应算法的三维程序,计算分析了三维柱体的拉伸和弯曲问题,并将计算结果与ABAQUS软件计算结果以及理论解进行了比较。结果表明,本文给出的耦合算法计算精度高,收敛性好,可以用以模拟裂纹扩展等问题。

In this paper,the finite element and meshless local Petrov-Galerkin（FEM/MLPG） coupling algorithm is presented based on the transformation matrix of finite element（TMF） and the transformation matrix of meshless method（TMM）,respectively.Three dimensional computer program of the proposed FEM/MLPG coupling method is developed,and it is used to analyze the bending and tension problems of a 3D post.The results obtained with the coupling method presented in this paper are compared with those determined by ABAQUS software and the theoretical solution.It is demonstrated that the FEM/MLPG coupling algorithm method behaves high computational precision and convergence,and the method can be used to efficiently simulate the dynamic propagation of cracks.