回転とひずみ自由度を有する四節点四面体要素の微圧縮材料に対する性能調査2025 · In this study, we investigate the accuracy of four-node tetrahedral elements with drilling and strain degrees of freedom (GNTet4) for nearly incompressible materials. GNTet4 is a one of the generalized finite element method approximation. Three types of GNTet4 are introduced by applying approximation polynomials of the Taylor expansion. First, we reveal the extra degrees of freedom constraints without the zero-energy modes of each GNTet4 through eigenvalue analysis. Next, the displacement accuracy of each GNTet4 is evaluated by analyzing a cantilever beam. The results shows that GNTet4, which approximates the third-order Taylor expansion (GNTet4-3rd), is almost identical to a 20-node tetrahedral element. Furthermore, a plane-strain compression test is performed to investigate the analytical accuracy of each GNTet4 for nearly incompressible materials. To analyze nearly incompressible materials with high accuracy, selective reduced integration (SRI) and third-order Taylor expansion must be applied to GNTet4 (GNTet4-3rd with SRI). Incidentally, the analysis accuracy of GNTet4-3rd with SRI is the same as or higher than that of the 10-node tetrahedral element (FEM-Tet10). Furthermore, the GNT4-3rd with SRI, which possess the nodal point at the element vertex only, suppressed the nodal oscillation. Thus, in nearly incompressible materials, to obtain the same analysis accuracy as that of FEM-Tet10, the four-node tetrahedral element must apply the displacement function of the fourth order and the SRI.
