On hexahedral finite element HC8/27 in elasticity

Abstract

A new three-dimensional multifield finite element approach for analysis of isotropic and anisotropic materials in linear elastostatics, derived from primal–mixed variational formulation based on Hellinger-Reissner’s principle, is presented. The novel properties are stress approximation by the continuous base functions, introduction of stress constraints as essential boundary conditions, and initial displacement and stress/strain field capability. It will be shown that resulting hexahedral finite element HC8/27 satisfies mathematical convergence requirements, like consistency and stability, even when it is rigorously slandered, distorted or used for the nearly incompressible materials. In order to minimise accuracy error and enable introductions of displacement and stress constraints, the tensorial character of the present finite element equations is fully respected. The proposed finite element is subjected to the number of standard pathological tests in order to test convergence of the results.