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Determination of an optimal shape of domain using the topological derivative and the Boundary Element Method

Freus K., Freus S.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 4

41--48

In the paper, the topological derivative for the Laplace equation is taken into account. The governing equation is solved by means of the Boundary Element Method. The topological-shape sensitivity method is used to determine the points showing the lowest sensitivities. On the selected points, material is eliminated by opening a hole, using the appropriate iterative process. This one is halted when a given amount of material is removed. The objective of this work is to obtain an optimal topology of the domain considered. In the final part of the paper, the example of computations is shown.

Crack detection by the topological gradient method

Amstutz S., Horchani I., Masmoudi M.

Control and Cybernetics

2005

Vol. 34, no 1

81-101

The topological sensitivity analysis consists in studying the behavior of a shape functional when modifying the topology of the domain. In general, the perturbation under consideration is the creation of a small hole. In this paper, the topological asymptotic expansion is obtained for the Laplace equation with respect to the insertion of a short crack inside a plane domain. This result is illustrated by some numerical experiments in the context of crack detection.