Displaying similar documents to “Relating phase field and sharp interface approaches to structural topology optimization”

Design-dependent loads in topology optimization

Blaise Bourdin, Antonin Chambolle (2010)

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  of a reference domain, and the complement of 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 , which is the total work of...

Global minimizer of the ground state for two phase conductors in low contrast regime

Antoine Laurain (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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The problem of distributing two conducting materials with a prescribed volume ratio in a ball so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions is considered in two and three dimensions. The gap between the two conductivities is assumed to be small (low contrast regime). The main result of the paper is to show, using asymptotic expansions with respect to and to small geometric perturbations of the optimal shape, that the global minimum of the...

Convex shape optimization for the least biharmonic Steklov eigenvalue

Pedro Ricardo Simão Antunes, Filippo Gazzola (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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The least Steklov eigenvalue for the biharmonic operator in bounded domains gives a bound for the positivity preserving property for the hinged plate problem, appears as a norm of a suitable trace operator, and gives the optimal constant to estimate the -norm of harmonic functions. These applications suggest to address the problem of minimizing in suitable classes of domains. We survey the existing results and conjectures about this topic;...

On shape optimization problems involving the fractional laplacian

Anne-Laure Dalibard, David Gérard-Varet (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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Our concern is the computation of optimal shapes in problems involving (−). We focus on the energy (Ω) associated to the solution of the basic Dirichlet problem ( − )  = 1 in Ω,  = 0 in Ω. We show that regular minimizers Ω of this energy under a volume constraint are disks. Our proof goes through the explicit computation of the shape derivative (that seems to be completely new in the fractional context), and a refined adaptation of the...