Hybrid level set phase field method for topology optimization of contact problems

Andrzej Myśliński; Konrad Koniarski

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 4, page 419-435
  • ISSN: 0862-7959

Abstract

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The paper deals with the analysis and the numerical solution of the topology optimization of system governed by variational inequalities using the combined level set and phase field rather than the standard level set approach. The standard level set method allows to evolve a given sharp interface but is not able to generate holes unless the topological derivative is used. The phase field method indicates the position of the interface in a blurry way but is flexible in the holes generation. In the paper a two-phase topology optimization problem is formulated in terms of the modified level set function and regularized using the Cahn-Hilliard based interfacial energy term rather than the standard perimeter term. The derivative formulae of the cost functional with respect to the level set function is calculated. Modified reaction-diffusion equation updating the level set function is derived. The necessary optimality condition for this optimization problem is formulated. The finite element and finite difference methods are used to discretize the state and adjoint systems. Numerical examples are provided and discussed.

How to cite

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Myśliński, Andrzej, and Koniarski, Konrad. "Hybrid level set phase field method for topology optimization of contact problems." Mathematica Bohemica 140.4 (2015): 419-435. <http://eudml.org/doc/271819>.

@article{Myśliński2015,
abstract = {The paper deals with the analysis and the numerical solution of the topology optimization of system governed by variational inequalities using the combined level set and phase field rather than the standard level set approach. The standard level set method allows to evolve a given sharp interface but is not able to generate holes unless the topological derivative is used. The phase field method indicates the position of the interface in a blurry way but is flexible in the holes generation. In the paper a two-phase topology optimization problem is formulated in terms of the modified level set function and regularized using the Cahn-Hilliard based interfacial energy term rather than the standard perimeter term. The derivative formulae of the cost functional with respect to the level set function is calculated. Modified reaction-diffusion equation updating the level set function is derived. The necessary optimality condition for this optimization problem is formulated. The finite element and finite difference methods are used to discretize the state and adjoint systems. Numerical examples are provided and discussed.},
author = {Myśliński, Andrzej, Koniarski, Konrad},
journal = {Mathematica Bohemica},
keywords = {topology optimization; unilateral problem; level set approach; phase field method},
language = {eng},
number = {4},
pages = {419-435},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Hybrid level set phase field method for topology optimization of contact problems},
url = {http://eudml.org/doc/271819},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Myśliński, Andrzej
AU - Koniarski, Konrad
TI - Hybrid level set phase field method for topology optimization of contact problems
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 4
SP - 419
EP - 435
AB - The paper deals with the analysis and the numerical solution of the topology optimization of system governed by variational inequalities using the combined level set and phase field rather than the standard level set approach. The standard level set method allows to evolve a given sharp interface but is not able to generate holes unless the topological derivative is used. The phase field method indicates the position of the interface in a blurry way but is flexible in the holes generation. In the paper a two-phase topology optimization problem is formulated in terms of the modified level set function and regularized using the Cahn-Hilliard based interfacial energy term rather than the standard perimeter term. The derivative formulae of the cost functional with respect to the level set function is calculated. Modified reaction-diffusion equation updating the level set function is derived. The necessary optimality condition for this optimization problem is formulated. The finite element and finite difference methods are used to discretize the state and adjoint systems. Numerical examples are provided and discussed.
LA - eng
KW - topology optimization; unilateral problem; level set approach; phase field method
UR - http://eudml.org/doc/271819
ER -

References

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