A method of constructing 2D $4$-node and 3D $8$-node finite elements for solving elasticity problems

D. T. Chekmarev

N. I. Lobachevski State University of Nizhni Novgorod, Faculty of Mechanics and Mathematics, Nizhni Novgorod, Russia

Abstract: A new method of constructing FEM schemes for solving 2D and 3D problems of continuum mechanics is proposed. The method is based on the projection of the rare mesh schemes of higher dimension linear finite elements on a 2D or 3D finite element mesh. Based on the example of a linear elasticity problem, the construction of 2D $4$-node and 3D $8$-node FEM schemes is considered. The obtained finite elements are similar to the known multilinear elements and are more efficient. The schemes contain parameters that make it possible to adjust the convergence of the numerical solutions. The possibility of applying this approach to the construction of numerical schemes for other problems of mathematical physics is shown.

Keywords: finite element method, rare mesh scheme, efficiency of numerical schemes, approximation, convergence of numerical solutions, elasticity theory.

UDC: 519.6+539.3

Received: 12.09.2013