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

Frédéric de Gournay; Grégoire Allaire; François Jouve

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 14, Issue: 1, page 43-70
- ISSN: 1292-8119

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topde Gournay, Frédéric, Allaire, Grégoire, and Jouve, François. "Shape and topology optimization of the robust compliance via the level set method." ESAIM: Control, Optimisation and Calculus of Variations 14.1 (2010): 43-70. <http://eudml.org/doc/90865>.

@article{deGournay2010,

abstract = {
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
compute it. Then, in the framework of Hadamard method, we
compute the directional shape derivative of this criterion which is
used in a numerical algorithm, based on the level set method,
to find optimal shapes that minimize the worst-case compliance.
Since this criterion is usually merely directionally differentiable,
we introduce a semidefinite programming approach to
select the best descent direction at each step of a
gradient method. Numerical examples are given in 2-d and 3-d.
},

author = {de Gournay, Frédéric, Allaire, Grégoire, Jouve, François},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Robust design;
worst-case design;
shape optimization;
topology optimization;
level set method;
semidefinite programming; robust design; worst-case design; shape optimization; topology optimization; level set method; semidefinite programming},

language = {eng},

month = {3},

number = {1},

pages = {43-70},

publisher = {EDP Sciences},

title = {Shape and topology optimization of the robust compliance via the level set method},

url = {http://eudml.org/doc/90865},

volume = {14},

year = {2010},

}

TY - JOUR

AU - de Gournay, Frédéric

AU - Allaire, Grégoire

AU - Jouve, François

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 14

IS - 1

SP - 43

EP - 70

AB -
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
compute it. Then, in the framework of Hadamard method, we
compute the directional shape derivative of this criterion which is
used in a numerical algorithm, based on the level set method,
to find optimal shapes that minimize the worst-case compliance.
Since this criterion is usually merely directionally differentiable,
we introduce a semidefinite programming approach to
select the best descent direction at each step of a
gradient method. Numerical examples are given in 2-d and 3-d.

LA - eng

KW - Robust design;
worst-case design;
shape optimization;
topology optimization;
level set method;
semidefinite programming; robust design; worst-case design; shape optimization; topology optimization; level set method; semidefinite programming

UR - http://eudml.org/doc/90865

ER -

## References

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