无网格Galerkin法与非协调元方法的耦合

Coupling of element-free Galerkin method and incompatible element method

无网格Galerkin法(EFGM)在处理不可压缩问题时不存在自锁现象,有限元方法(FEM)也常被用来与其耦合以方便地施加边界条件和提高计算效率。在有限元方法中使用等参元,EFGM与FEM的耦合方法在处理不可压缩问题时仍然存在自锁现象。本文在有限元方法中,采用非协调元,将无网格Galerkin法与非协调元耦合,保留了耦合方法的优点,且避免了求解不可压缩问题时的自锁现象。算例显示本文方法在分析平面应变不可压缩问题时能得到合理的结果。

Incompatible element method is used to couple with element-free Galerkin method (EFGM). EFGM do not exhibit any locking when it is used to analyze the nearly incompressible materials. The finite element method (FEM) is coupled with EFGM so that the essential boundary conditions can be imposed easily. However, when the isoparametric elements are used in FEM, the coupled method still exhibits locking. Because the incompatible element method do not exhibit any locking, incompatible elements are used in FEM to hold the above-mentioned advantages of the coupled method and avoid locking as well as. Numerical examples show that the method can pass the patch test, and the displacement locking and stress instability can be avoided in incompressible calculation and reasonable results can be achieved.