On the Features of a Moment Finite Element for 3D Elasticity Problems Based on Rare Mesh FEM Scheme

The convergence of FEM schemes is connected with the mutual arrangement of the finite elements. A good result was shown by the arrangement of linear tetrahedral 4-node elements in the centers of cells of the hexahedral mesh and the remaining four elements are not involved in the calculations. This scheme was used to 3D dynamic elasticity and plasticity problems and showed its best performance. Generalizing this approach to arbitrary dimension, we obtain schemes based on a linear finite element in the form of an n-dimensional simplex inscribed in an n-dimensional cube. Further development of this idea is associated with the projection of schemes from spaces of higher dimension onto a grid of lower dimension. In this way, a 3D 8-node finite element is constructed. The features of this finite element and its advantages over traditional finite elements are considered.