Novel approach for devising higher-order hybrid elements

Abstract

This paper presents an efficient way to devise higher-order hybrid elements by generalizing the admissible matrix formulation recently proposed by the author. The assumed stress or strain is first decomposed into the constant, lower- and higher-order modes. In the absence of any higher-order modes, the resulting hybrid element would be identical to the corresponding sub-integrated displacement element. By a natural and straightforward method of orthogonalizing the higher-order modes with respect to the constant and lower-order modes, the element stiffness can be partitioned into a lower- and a higher-order matrix. With further refinements, the method devised can readily be applied to a number of higher-order hybrid elements with enhanced finite element consistency and computational efficiency.