Efficient hybrid/mixed elements using admissible matrix formulation

Abstract The potential applications of the conceptual idea initiated by Bergan and Hanssen in designing efficient hybrid/mixed elements are described. Applications based on the extended Hellinger-Reissner and Hu-Washizu principles with the inclusion of the non-conforming displacement components are discussed. By rationally choosing the stress/strain interpolants and incorporating the admissible matrix formulation justified by the patch test consideration, the computational cost involved in matrix inversions and manipulations can effectively be reduced. Three-dimensional solid elements are given as illustrations of the proposed methodology. All the proposed elements yield satisfactory accuracy compared to other hybrid elements in the open literature.

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