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Invariant 8‐node hybrid‐stress elements for thin and moderately thick plates
Author(s) -
Spilker R. L.
Publication year - 1982
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.1620180805
Subject(s) - invariant (physics) , node (physics) , stress (linguistics) , mathematics , displacement (psychology) , finite element method , structural engineering , mathematical analysis , geometry , engineering , psychology , linguistics , philosophy , mathematical physics , psychotherapist
Eight‐node hybrid‐stress elements are developed for the analysis of plates ranging from arbitrarily thin to moderately thick. The displacement behaviour is characterized by a transverse displacement and independent cross‐section rotations, which are interpolated using the 8‐node Serendipity shape functions. All components of stress are included; alternative elements are developed which differe in the form of the inplane distribution of the stresses. Elements are sought for whic the stiffiness is invariant and of correct rank, and whic show on signs of deterioration in the thin‐plate limit. A discussion of the prospects for developing a 4‐node element with these characteristics is also presented. Example problems are used to compare the performance of the 8‐node elements including convergence behaviour, intraelement stress distributions and optimal sampling locations, and range of applicability in terms of plate thickness ratio.