A Variational Method for Inclusion and Indentation Problems
- 1 June 1969
- journal article
- research article
- Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics
- Vol. 5 (2) , 194-205
- https://doi.org/10.1093/imamat/5.2.194
Abstract
This paper considers a variational principle for Fredholm integral equations in which the range of integration is fixed but unknown. Equations of this type occur in the study of inclusion and indentation problems in the theory of elasticity. It is shown that a functional associated with the integral equation is stationary with respect to variations of the range of integration around its exact value. The method is applied to indentation problems and to cylindrical and spherical inclusion problems. Where a comparison is possible, the present results agree closely with those obtained by other methods.Keywords
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