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Efficient formulation of robust hybrid elements using orthogonal stress/strain interpolants and admissible matrix formulation
Author(s) -
Sze K. Y.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620350102
Subject(s) - covariance and contravariance of vectors , hexahedron , mathematics , matrix (chemical analysis) , invariant (physics) , correctness , merge (version control) , algorithm , algebra over a field , mathematical analysis , pure mathematics , computer science , finite element method , structural engineering , engineering , materials science , information retrieval , composite material , mathematical physics
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 hexahédral 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.