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A Twelvth Order Theory of Transverse Bending of Transversely Isotropic Plates
Author(s) -
Reissner E.
Publication year - 1983
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.19830630706
Subject(s) - transverse isotropy , boundary value problem , isotropy , mathematical analysis , transverse plane , order (exchange) , polar coordinate system , mathematics , bending , laplace transform , stress (linguistics) , geometry , physics , structural engineering , optics , engineering , finance , economics , linguistics , philosophy , thermodynamics
Motivated by the problem of the differences between stress and stress couple concentration factors for transverse bending of plates with small circular holes we use a variational method for the derivation of a twelfth order two‐dimensional theory of transversely isotropic plates, which includes the known sixth order theory of sheardeformable plates as a special case via constitutive‐coefficient specialization. It is further shown that the twelvth order system may be reduced in a non‐obvious way to two simultaneous second order and two simultaneous fourth order Laplace operator equations, with this then making it possible to obtain closed form solutions for polar coordinate boundary value problems.