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Displaying similar documents to “On variations of the shape Hessian and sufficient conditions for the stability of critical shapes.”

About stability of equilibrium shapes

Marc Dambrine, Michel Pierre (2000)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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On the ersatz material approximation in level-set methods

Marc Dambrine, Djalil Kateb (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire , (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic...

About stability of equilibrium shapes

Marc Dambrine, Michel Pierre (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We discuss the stability of "critical" or "equilibrium" shapes of a shape-dependent energy functional. We analyze a problem arising when looking at the positivity of the second derivative in order to prove that a critical shape is an optimal shape. Indeed, often when positivity -or coercivity- holds, it does for a weaker norm than the norm for which the functional is twice differentiable and local optimality cannot be deduced. We solve this problem for a particular but significant...