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A hybrid strain finite element for plates and shells
Author(s) -
Bergmann V. L.,
Mukherjee S.
Publication year - 1990
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.1620300203
Subject(s) - quadrilateral , finite element method , bilinear interpolation , mathematics , interpolation (computer graphics) , displacement field , plane stress , mathematical analysis , stress resultants , displacement (psychology) , geometry , linear interpolation , variational principle , linear elasticity , shell (structure) , structural engineering , engineering , physics , classical mechanics , motion (physics) , psychology , statistics , civil engineering , polynomial , psychotherapist
This paper describes a new hybrid strain finite element for geometrically linear analysis of plates and shells. The formulation for materially linear problems is based on a mixed variational principle having strain and displacement rates as independently varied fields. To facilitate extension to materially non‐linear analysis, the variational principle is used in rate form and the plane stress assumption is not imposed a priori in the formulation. When desired, the plane stress assumption is imposed in a manner similar to imposition of fixed boundary conditions. The element geometry is based on a nine‐noded quadrilateral with biquadratic interpolation of the displacement field. The strain field is based on a bilinear interpolation with additional non‐linear terms, chosen on the basis of eigenvalue analysis. The element passes the required patch tests, does not display either membrane or shear locking effects, and is free of communicable spurious modes. Numerical results are presented for elastic analyses of several standard plate and shell test problems.