Performance evaluation of three-node triangular element based on generalized finite element method approximation for nearly incompressible materials

Abstract

Rigid plastic and large deformation analyses of the finite element method (FEM) require multiple remeshing procedures to avoid a decrease in the analysis accuracy. Thus, a three-node triangular element that can perform automatic mesh generation is suitable for these FEM analyses. However, in the FEM analysis of nearly incompressible materials using the displacement-based three-node triangular element, the inhibition of volumetric locking and pressure checkerboarding is required. The generalized finite element method (GFEM) approximation can improve the analysis accuracy for three-node triangular elements without the addition of midpoint nodes. In this study, we performed a detailed performance evaluation of a three-node triangular element based on the GFEM approximation for nearly incompressible materials in the linear elastic analysis. The GFEM approximation employs a polynomial of degree 1–3. Performance investigation using a compression test revealed that each GFEM element required the application of selective reduced integration to avoid volumetric locking and pressure checkerboarding. Furthermore, we investigated the number of constraint degrees of freedom of the GFEM element, which is related to volumetric locking. In the case of the GFEM element, we inferred that the application of this investigation is difficult because of the additional nodal degrees of freedom, which are different from the translational nodal displacement.

Keywords

• generalized finite element method
• three-node triangular element
• displacement-based finite element method
• volumetric locking
• pressure checkerboarding