Differentiation of energy functionals in the three-dimensional theory of elasticity for bodies with surface cracks |
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Authors: | E M Rudoi |
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Institution: | (1) Lavrent’ev Institute of Hydrodynamics, pr. Akad. Lavrent’eva 15, Novosibirsk, 630090, Russia |
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Abstract: | A three-dimensional elastic body with a surface crack is considered. The boundary nonpenetration conditions in the form of inequalities (the Signorini type conditions) are given at the faces of the crack. The convergence is proved of a sequence of equilibrium problems in perturbed domains to the solution of an equilibrium problem in the unperturbed domain in a suitable Sobolev function space. The derivative is calculated of the energy functional with respect to the perturbation parameter of the surface crack. |
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