A moment theory of elastic plates
作者:
R. Tiffen,
F. P. Sayer,
期刊:
Mathematika
(WILEY Available online 1962)
卷期:
Volume 9,
issue 1
页码: 11-24
ISSN:0025-5793
年代: 1962
DOI:10.1112/S0025579300003053
出版商: London Mathematical Society
数据来源: WILEY
摘要:
SummaryThis 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 stressestα3, 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.
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