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On the Equations of Linear Shallow Shell Theory
Author(s) -
Reissner E.,
Wan F. Y. M.
Publication year - 1969
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1969482133
Subject(s) - shell theory , shell (structure) , transverse shear , transverse plane , duality (order theory) , surface (topology) , mathematical analysis , mathematics , spherical shell , bending moment , shear (geology) , geometry , classical mechanics , physics , structural engineering , materials science , engineering , discrete mathematics , composite material , thermodynamics
The paper presents a formulation of the two‐dimensional theory of shallow shells, including the effects of transverse shear deformation and of moments turning about the normal to the middle surface. The present formulation includes, as it must, Marguerre's theory. At the same time it is consistent with recent formulations of general linear shell theory, in particular in regard to the preservation of the static‐geometric duality. Various reductions of the equation of the theory are considered. Of particular significance and effectiveness among these are reductions for the special cases of (1) shells without moments about the middle surface normal, (where an earlier result of Naghdi is extended) (2) the shell without transverse shear deformability, (the static‐geometrical dual of case (1)). As an application of the general equations an explicit solution is obtained for the problem of stretching, twisting and bending of pretwisted rectangular plates.