Displaying similar documents to “On the shape of solutions to some variational problems”

Design-dependent loads in topology optimization

Blaise Bourdin, Antonin Chambolle (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset S of a reference domain, and the complement of S is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure S , which is the total work of the...

Numerical minimization of eigenmodes of a membrane with respect to the domain

Édouard Oudet (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.