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Plate theories via energy potentials
Author(s) -
Wempner G.
Publication year - 1968
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/zamm.19680480706
Subject(s) - constitutive equation , interpretation (philosophy) , buckling , stress (linguistics) , displacement (psychology) , basis (linear algebra) , classical mechanics , mathematics , potential energy , mathematical analysis , calculus (dental) , physics , finite element method , structural engineering , computer science , engineering , geometry , psychotherapist , programming language , medicine , linguistics , philosophy , dentistry , psychology
A direct approach to the derivation of plate theories focuses on the transition from three‐dimensional to two‐dimensional constitutive equations. Alternatively, approximations of the displacement or stress distributions can serve as the basis of a theory. The derivation is accomplished by integrating a strain‐energy potential through the thickness. Since the approach does not preclude finite rotations, the resulting constitutive equations are applicable to buckling and postbuckling. A broader interpretation is given to the strain‐measures of the Reissner theory. The complementary alternatives are illustrated by examples, one leading to the Reissner result.