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From Reissner Plate Theory to Three Dimensions in Large Deformation Shell Analysis
Author(s) -
Ramm E.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(200001)80:1<61::aid-zamm61>3.0.co;2-e
Subject(s) - finite element method , shell (structure) , plate theory , context (archaeology) , deformation (meteorology) , shell theory , constitutive equation , shear (geology) , classical mechanics , variational principle , geometry , physics , mathematics , mathematical analysis , structural engineering , engineering , materials science , geology , mechanical engineering , composite material , paleontology , meteorology
The paper first focuses on the historical context in which Reissner's famous shear deformation plate theory was derived. Here essentially Eric R eissner 's own view on this matter, in particular the relation to Mindlin's contribution, is followed [15]. The significance of shear deformable plate and shell theories for the derivation of finite elements is briefly described. As a major aspect it is shown how these formulations can be easily extended to a completely three‐dimensional model allowing to apply unmodified 3D constitutive equations and to include large strain effects but keeping the essential features of a thin‐walled structure. Finally, the importance of Reissner's variational principle for the development of hybrid finite element models is pointed out.