Risk averse elastic shape optimization with parametrized fine scale geometry

Geihe, Benedict; Lenz, Martin; Rumpf, Martin; Schultz, Rüdiger

doi:10.1007/s10107-012-0531-1

Cited by 10 publications

(2 citation statements)

References 27 publications

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“…In [12,24] risk neutral and risk averse stochastic shape optimization were discussed for mean-risk models with the above specifications. To this end the stochastic energies were used as stochastic cost functions for shape optimization directly.…”

Section: Shape Optimization With Stochastic Loadingmentioning

confidence: 99%

Stochastic Dominance Constraints in Elastic Shape Optimization

Conti¹,

Rumpf²,

Schultz³

et al. 2018

SIAM J. Control Optim.

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This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from finite-dimensional stochastic programming to shape optimization. Rather than handling risk aversion in the objective, this enables risk aversion by including dominance constraints that single out subsets of nonanticipative shapes which compare favorably to a chosen stochastic benchmark. This new class of stochastic shape optimization problems arises by optimizing over such feasible sets. The analytical description is built on risk-averse cost measures. The underlying cost functional is of compliance type plus a perimeter term, in the implementation shapes are represented by a phase field which permits an easy estimate of a regularized perimeter. The analytical description and the numerical implementation of dominance constraints are built on risk-averse measures for the cost functional. A suitable numerical discretization is obtained using finite elements both for the displacement and the phase field function. Different numerical experiments demonstrate the potential of the proposed stochastic shape optimization model and in particular the impact of high variability of forces or probabilities in the different realizations.

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Section: Shape Optimization With Stochastic Loadingmentioning

confidence: 99%

Stochastic Dominance Constraints in Elastic Shape Optimization

Conti¹,

Rumpf²,

Schultz³

et al. 2018

SIAM J. Control Optim.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Several approaches have been explored to optimize such structures. Geihe and al [10] work on the set of square cells with parametrized elliptic holes and rewrite the topology optimization problem as a parametric one. Other methods are based on the Simplified Isotropic Material with Penalization (SIMP) method [6].…”

Section: Introductionmentioning

confidence: 99%