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A new drilling quadrilateral membrane element with high coarse‐mesh accuracy using a modified Hu‐Washizu principle
Author(s) -
Chang T. L.,
Lee C.L.,
Carr A. J.,
Dhakal R. P.,
Pampanin S.
Publication year - 2019
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.6066
Subject(s) - quadrilateral , polygon mesh , displacement (psychology) , finite element method , displacement field , variational principle , mathematics , node (physics) , degrees of freedom (physics and chemistry) , mathematical analysis , topology (electrical circuits) , structural engineering , geometry , engineering , physics , psychology , quantum mechanics , combinatorics , psychotherapist
Summary By utilizing a modified Hu‐Washizu principle, a new mixed variational framework and a corresponding high‐performing four‐node membrane element with drilling degrees of freedom, named as GCMQ element, are proposed. In this work, the generalized conforming concept, which is originally proposed within a displacement‐based formulation, is extended to a mixed formulation. The new element is able to handle higher‐order displacement, strain, and stress distributions. The interpolations are complete up to second order for stress and strain. The enhanced strain field is optimized so that a complete cubic displacement field can be represented. For numerical integration, a five‐point scheme is proposed to minimize computational cost. Compared to other four‐node elements in existing literature, numerical examples show that the proposed element has a better performance regarding predictions of both displacements and internal forces, particularly with coarse meshes. The new element is also free from shear locking and volumetric locking. Due to the nature of the mixed framework, GCMQ can be directly used in elastoplastic applications.

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