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

✍ Scribed by Yi-Yuan Yu

Publisher
Elsevier Science
Year
1955
Tongue
English
Weight
596 KB
Volume
260
Category
Article
ISSN
0016-0032

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✦ Synopsis

The paper constitutes a generalization of the complex variable method developed by Musehelisvili 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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## Abstract We consider the buckling problem for a family of thin plates with thickness parameter __Ξ΅__. This involves finding the least positive multiple __Ξ»__ of the load that makes the plate __buckle__, a value that can be expressed in terms of an eigenvalue problem involving a non‐compact opera