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On the complex representation of the general extensional and flexural problems of thin plates and their analogies

Authors
Journal
Journal of the Franklin Institute
0016-0032
Publisher
Elsevier
Publication Date
Volume
260
Issue
4
Identifiers
DOI: 10.1016/0016-0032(55)90873-5

Abstract

Abstract The paper constitutes a generalization of the complex variable method developed by Muschelisvili and Lechnitzky for solving the extensional and flexural problems of thin plates to include, respectively, the effect of the body force and the lateral load. The two usual analogies between the two types of problems are also established in a quantitative manner for these general cases; and, as was observed by Southwell, the two analogies may be combined into one with the reversal of the sign of Poisson's ratio. As illustrations, several circular plate problems are solved by means of the generalized boundary equations derived, and the corresponding analogous problems of some of these are determined by means of the analogies. As a necessity, a relation is established first between the indefinite integral and the line integral of a non-analytic function in the complex plane.

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