Displaying similar documents to “Some new problems in spectral optimization”

Shape and topology optimization of the robust compliance the level set method

Frédéric de Gournay, Grégoire Allaire, François Jouve (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The goal of this paper is to study the so-called worst-case or robust optimal design problem for minimal compliance. In the context of linear elasticity we seek an optimal shape which minimizes the largest, or worst, compliance when the loads are subject to some unknown perturbations. We first prove that, for a fixed shape, there exists indeed a worst perturbation (possibly non unique) that we characterize as the maximizer of a nonlinear energy. We also propose a stable algorithm...

Shape and topology optimization of the robust compliance via the level set method

François Jouve, Grégoire Allaire, Frédéric de Gournay (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

The goal of this paper is to study the so-called worst-case or robust optimal design problem for minimal compliance. In the context of linear elasticity we seek an optimal shape which minimizes the largest, or worst, compliance when the loads are subject to some unknown perturbations. We first prove that, for a fixed shape, there exists indeed a worst perturbation (possibly non unique) that we characterize as the maximizer of a nonlinear energy. We also propose a stable algorithm to...

Optimal design of cylindrical shells

Peter Nestler, Werner H. Schmidt (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The present paper studies an optimization problem of dynamically loaded cylindrical tubes. This is a problem of linear elasticity theory. As we search for the optimal thickness of the tube which minimizes the displacement under forces, this is a problem of shape optimization. The mathematical model is given by a differential equation (ODE and PDE, respectively); the mechanical problem is described as an optimal control problem. We consider both the stationary (time independent) and the...