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Stress oscillations in plane stress modelling of flexure—a field‐consistency interpretation
Author(s) -
Prathap G.,
Subramanian G.,
Babu C. Ramesh
Publication year - 1987
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.1620240405
Subject(s) - finite element method , spurious relationship , computation , plane stress , shear (geology) , stress field , consistency (knowledge bases) , shear stress , structural engineering , stress (linguistics) , mechanics , mathematics , physics , geometry , engineering , algorithm , materials science , linguistics , statistics , philosophy , composite material
Exactly integrated isoparametric plane stress elements behave poorly in flexure. The 4‐noded element ‘locks’, with errors that progress indefinitely as element aspect ratio increases. Reduced integration of the shear strain energy eliminates this locking entirely. The 8‐noded element does not lock, but improves in performance with reduced integration of shear strain energy. Both elements, with their original shape functions, show severe shear stress oscillations in flexure. In this paper we attribute these oscillations to the lack of ‘consistency’ of shear strain fields derived directly from independent field‐variable interpolations. We derive error models for specific tractable examples which can confirm the accuracy of this conceptual scheme through digital computation using the finite element models. A field‐consistent redistribution strategy for the shear strain field is offered as an elegant procedure to free the elements of spurious oscillations and give a ‘lock’‐free performance.