Efficient formulation of robust hybrid elements using orthogonal stress/strain interpolants and admissible matrix formulation

Abstract

This paper presents an investigation of using orthogonal constant and higher order stress modes in formulating efficient hybrid elements by equipping the primary idea of Bergan and Hanssen. Two sample elements modified from Pian-Sumihara 5-β plane and Pian-Tong 18-β hexahedral assumed contravariant stress elements are derived. With the suggested admissible simplifications of the flexibility matrices incorporated into the two new elements, new plane and hexahedral elements requiring respectively no and a negligible amount of computing efforts for inverting the flexibility matrices are formed. All, proposed elements are stable, invariant, contain no empirically determined factor and strictly pass the patch test. Popular benchmark problems are studied and the accuracy of the proposed elements is close to their parent models.