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A moment theory of elastic plates
Author(s) -
Tiffen R.,
Sayer F. P.
Publication year - 1962
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300003053
Subject(s) - mathematics , mathematical analysis , isotropy , infinitesimal , moment (physics) , boundary value problem , transverse plane , quadratic equation , homogeneous , differential equation , geometry , classical mechanics , physics , structural engineering , quantum mechanics , combinatorics , engineering
Summary This paper is concerned with infinitesimal transverse displacements of homogeneous isotropic elastic plates. The method uses moments of the fundamental equations of orders 0, 1, 2, 3. Assuming a form for the shear stresses t α3 , these equations enable one to determine the mean values of the transverse displacements instead of the weighted mean values associated with plate theories of all but the classical type. The relevant moments of the stresses and displacements are expressed in terms of three functions satisfying three differential equations of the fourth order, the solutions of which may be expressed in terms of six independent functions. Thus six boundary conditions may be satisfied. Equating two, three and four of the above functions to zero in turn gives plate theories involving four, three and two boundary conditions respectively. The method is illustrated by assuming that the shear stresses are quadratic functions of the distance from the mid‐plane of the material.