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Shape and topological sensitivity analysis in domains with cracks

Alexander Khludnev;  Jan Sokołowski;  Katarzyna Szulc — 2010

Applications of Mathematics

The framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. The equilibrium problem for the elastic body with cracks is considered. Inequality type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. Modelling of such problems in two spatial dimensions is presented with all necessary details for further applications in shape optimization in structural...

Topological derivatives for semilinear elliptic equations

Mohamed Iguernane;  Serguei A. Nazarov;  Jean-Rodolphe Roche;  Jan Sokolowski;  Katarzyna Szulc — 2009

International Journal of Applied Mathematics and Computer Science

The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L∞ norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.

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