A first order approach for worst-case shape optimization of the compliance for a mixture in the low contrast regime

Dambrine, Marc; Laurain, Antoine

doi:10.1007/s00158-015-1384-z

Cited by 5 publications

(2 citation statements)

References 20 publications

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“…To ensure well-posedness of the stochastic problem, either an order must be defined on the relevant random variables, as in [11], or the problem needs to be transformed to a deterministic one by means of a probability measure. One possibility is to compute the worst case design [4,14]. Another possibility is to use first and second order moments to cast the problem in a deterministic setting [13]; this is particularly relevant if the probability distribution of the underlying random variable is unknown.…”

Section: Introductionmentioning

confidence: 99%

Stochastic approximation for optimization in shape spaces

Geiersbach¹,

Loayza-Romero²,

Welker³

2020

Preprint

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In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the method on Riemannian manifolds and then make the connection to shape spaces. The method is demonstrated on a model shape optimization problem from interface identification. Uncertainty arises in the form of a random partial differential equation, where underlying probability distributions of the random coefficients and inputs are assumed to be known. We verify some conditions for convergence for the model problem and demonstrate the method numerically.

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Section: Introductionmentioning

confidence: 99%

Stochastic approximation for optimization in shape spaces

Geiersbach¹,

Loayza-Romero²,

Welker³

2020

Preprint

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“…Several works deal about the problem of minimizing the compliance of the structure where standard boundary conditions are imposed on the free boundary. We can here mention the recent works of Allaire et al [6], Amstutz et al [8], Novotny et al [41] and Dambrine et al [24]. This list of references is far from being exhaustive and we also refer to the books of Sokolowski et al [45], of Henrot et al [35], of Allaire [3,4] and of Haslinger et al [33] for background notions about shape optimization methods.…”

Section: Introduction and General Notationsmentioning

confidence: 99%

Shape Sensitivity Analysis for Elastic Structures with Generalized Impedance Boundary Conditions of the Wentzell Type—Application to Compliance Minimization

Caubet

Kateb

Louër

2018

J Elast

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To cite this version:Fabien Caubet, Djalil Kateb, Frédérique Le Louër. Shape sensitivity analysis for elastic structures with generalized impedance boundary conditions of the Wentzell type -Application to compliance minimization. Journal of Elasticity, Springer Verlag, In press, Journal of Elasticity. Abstract This paper focuses on Generalized Impedance Boundary Conditions (GIBC) with second order derivatives in the context of linear elasticity and general curved interfaces. A condition of the Wentzell type modeling thin layer coatings on some elastic structure is obtained through an asymptotic analysis of order one of the transmission problem at the thin layer interfaces with respect to the thickness parameter. We prove the well-posedness of the approximate problem and the theoretical quadratic accuracy of the boundary conditions. Then we perform a shape sensitivity analysis of the GIBC model in order to study a shape optimization/optimal design problem. We prove the existence and characterize the first shape derivative of this model. A comparison with the asymptotic expansion of the first shape derivative associated to the original thin layer transmission problem shows that we can interchange the asymptotic and shape derivative analysis. Finally we apply these results to the compliance minimization problem. We compute the shape derivative of the compliance in this context and present some numerical simulations.

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Support-free robust topology optimization based on pseudo-inverse stiffness matrix and eigenvalue analysis

Fukada

2019

Struct Multidisc Optim

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A first order approach for worst-case shape optimization of the compliance for a mixture in the low contrast regime

Cited by 5 publications

References 20 publications

Stochastic approximation for optimization in shape spaces

Stochastic approximation for optimization in shape spaces

Shape Sensitivity Analysis for Elastic Structures with Generalized Impedance Boundary Conditions of the Wentzell Type—Application to Compliance Minimization

Support-free robust topology optimization based on pseudo-inverse stiffness matrix and eigenvalue analysis

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