# Topology optimization of quasistatic contact problems

• Volume: 22, Issue: 2, page 269-280
• ISSN: 1641-876X

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## Abstract

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This paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimization problem considered is to find the optimal material distribution inside a design domain occupied by the body in unilateral contact with the rigid foundation to obtain the optimally shaped domain for which the normal contact stress along the contact boundary is minimized. The volume of the body is assumed to be bounded. Using the material derivative and asymptotic expansion methods as well as the results concerning the differentiability of solutions to quasistatic variational inequalities, the topological derivative of the shape functional is calculated and a necessary optimality condition is formulated.

## How to cite

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Andrzej Myśliński. "Topology optimization of quasistatic contact problems." International Journal of Applied Mathematics and Computer Science 22.2 (2012): 269-280. <http://eudml.org/doc/208107>.

@article{AndrzejMyśliński2012,
abstract = {This paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimization problem considered is to find the optimal material distribution inside a design domain occupied by the body in unilateral contact with the rigid foundation to obtain the optimally shaped domain for which the normal contact stress along the contact boundary is minimized. The volume of the body is assumed to be bounded. Using the material derivative and asymptotic expansion methods as well as the results concerning the differentiability of solutions to quasistatic variational inequalities, the topological derivative of the shape functional is calculated and a necessary optimality condition is formulated.},
author = {Andrzej Myśliński},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {quasistatic contact problem; elasticity; Tresca friction; topology optimization},
language = {eng},
number = {2},
pages = {269-280},
title = {Topology optimization of quasistatic contact problems},
url = {http://eudml.org/doc/208107},
volume = {22},
year = {2012},
}

TY - JOUR
AU - Andrzej Myśliński
TI - Topology optimization of quasistatic contact problems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2012
VL - 22
IS - 2
SP - 269
EP - 280
AB - This paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimization problem considered is to find the optimal material distribution inside a design domain occupied by the body in unilateral contact with the rigid foundation to obtain the optimally shaped domain for which the normal contact stress along the contact boundary is minimized. The volume of the body is assumed to be bounded. Using the material derivative and asymptotic expansion methods as well as the results concerning the differentiability of solutions to quasistatic variational inequalities, the topological derivative of the shape functional is calculated and a necessary optimality condition is formulated.
LA - eng
KW - quasistatic contact problem; elasticity; Tresca friction; topology optimization
UR - http://eudml.org/doc/208107
ER -

## References

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