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An optimally integrated four‐node quadrilateral plate bending element
Author(s) -
Prathap G.,
Viswanath S.
Publication year - 1983
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.1620190606
Subject(s) - quadrilateral , shear (geology) , numerical integration , gaussian , bending of plates , point (geometry) , structural engineering , geometry , bending , node (physics) , finite element method , mathematics , mathematical analysis , topology (electrical circuits) , engineering , materials science , physics , composite material , combinatorics , quantum mechanics
A clearer understanding of the problems associated with reduced integration and optimum integration schemes for the development of Mindlin plate elements is presented. It is shown that an optimal selective integration rule can be found for the 4‐node quadrilateral plate bending element which requires 2 × 2 Gaussian integration for bending energy and 1 × 2 and 2 × 1 rules for the shear energy terms from (θ x − w , x ) and (θ y − w , y ), respectively. This will give an element of correct rank, without any zero energy mechanisms and without shear locking in the thin plate limit, and better performance in moderately thick situations than the currently available 4‐node quadrilaterals using one‐point shear integration or modified one‐point shear integration due to Hughes et al. The effects of arbitrary orientation of the grid and the non‐rectangular form of element are discussed.