Development of second-order three-node triangular element with drilling and strain degrees of freedom

In this study, a second-order three-node triangular element with drilling and strain degrees of freedom (DOF) (GNTri3-2nd) was developed. GNTri3-2nd was formulated by applying an approximation of the generalized finite element method and a second-order Taylor expansion. The boundary conditions of the extra nodal DOF (drilling, normal strain, and curvature) without the zero-energy mode are discussed through eigenvalue analysis. The analysis accuracy of GNTri3-2nd was higher than that of the conventional six-node triangular element (FEM-Tri6) for the cantilever problem. Furthermore, in the case of plane-strain compression with a nearly incompressible material, the analysis performance of GNTri3-2nd was almost identical to that of FEM-Tri6 when a selective reduced integration was applied to the element stiffness matrix. Finally, we applied the GNTri3-2nd to the fundamental rigid-plastic finite element method. The analysis result of GNTri3-2nd is in good agreement with the slip line method and the conventional four-node quadrilateral element.