# Topology optimization of systems governed by variational inequalities

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2010)

- Volume: 30, Issue: 2, page 237-252
- ISSN: 1509-9407

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topAndrzej Myśliński. "Topology optimization of systems governed by variational inequalities." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 30.2 (2010): 237-252. <http://eudml.org/doc/271166>.

@article{AndrzejMyśliński2010,

abstract = {This paper deals with the formulation of the necessary optimality condition for a topology optimization problem of an elastic body in unilateral contact with a rigid foundation. In the contact problem of Tresca, a given friction is governed by an elliptic variational inequality of the second order. The optimization problem consists in finding such topology of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. The topological derivative of the cost functional is calculated and a necessary optimality condition is formulated. The calculated topological derivative is also used in the numerical algorithm to find a descent direction by inserting voids in the domain occupied by the body. Numerical examples are provided.},

author = {Andrzej Myśliński},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {variational inequality; topology optimization},

language = {eng},

number = {2},

pages = {237-252},

title = {Topology optimization of systems governed by variational inequalities},

url = {http://eudml.org/doc/271166},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Andrzej Myśliński

TI - Topology optimization of systems governed by variational inequalities

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2010

VL - 30

IS - 2

SP - 237

EP - 252

AB - This paper deals with the formulation of the necessary optimality condition for a topology optimization problem of an elastic body in unilateral contact with a rigid foundation. In the contact problem of Tresca, a given friction is governed by an elliptic variational inequality of the second order. The optimization problem consists in finding such topology of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. The topological derivative of the cost functional is calculated and a necessary optimality condition is formulated. The calculated topological derivative is also used in the numerical algorithm to find a descent direction by inserting voids in the domain occupied by the body. Numerical examples are provided.

LA - eng

KW - variational inequality; topology optimization

UR - http://eudml.org/doc/271166

ER -

## References

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- [10] A.A. Novotny, R.A. Feijóo, C. Padra and E. Tarocco, Topological derivative for linear elastic plate bending problems, Control and Cybernetics 34 (2005), 339-361. Zbl1167.74487
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- [13] J. Sokołowski and J.P. Zolesio, Introduction to shape optimization. Shape sensitivity analysis, Berlin, Springer, 1992. Zbl0761.73003

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