Ivan Hlaváček, Jan Chleboun (1996)
Applications of Mathematics
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A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.
Samuel Amstutz (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.
Piotr Fulmański, Antoine Laurain, Jean-Francois Scheid, Jan Sokołowski (2007)
International Journal of Applied Mathematics and Computer Science
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The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed...
Maatoug Hassine, Philippe Guillaume (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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The gradient based topological optimization tools introduced during the last ten years tend naturally to modify the topology of a domain by creating small holes inside the domain. Once these holes have been created, they usually remain unchanged, at least during the topological phase of the optimization algorithm. In this paper, a new asymptotic expansion is introduced which allows to decide whether an existing hole must be removed or not for improving the cost function. Then, two numerical...