An integral equation approach to boundary value problems of classical elastostatics

Author:
Frank J. Rizzo

Journal:
Quart. Appl. Math. **25** (1967), 83-95

DOI:
https://doi.org/10.1090/qam/99907

MathSciNet review:
QAM99907

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Abstract | References | Additional Information

Abstract: The analogy between potential theory and classical elasticity suggests an extension of the powerful method of integral equations to the boundary value problems of elasticity. A vector boundary formula relating the boundary values of displacement and traction for the general equilibrated stress state is derived. The vector formula itself is shown to generate integral equations for the solution of the traction, displacement, and mixed boundary value problems of plane elasticity. However, an outstanding conceptual advantage of the formulation is that it is not restricted to two dimensions. This distinguishes it from the methods of Muskhelishvili and most other familiar integral equation methods. The presented approach is a real variable one and is applicable, without inherent restriction, to multiply connected domains. More precisely, no difficulty of the order of determining a mapping function is present and unwanted Volterra type dislocation solutions are eliminated a priori. An indication of techniques necessary to effect numerical solution of the resulting integral equations is presented with numerical data from a set of test problems.

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Additional Information

DOI:
https://doi.org/10.1090/qam/99907

Article copyright:
© Copyright 1967
American Mathematical Society