Design-dependent loads in topology optimization

Blaise Bourdin; Antonin Chambolle

ESAIM: Control, Optimisation and Calculus of Variations (2003)

  • Volume: 9, page 19-48
  • ISSN: 1292-8119

Abstract

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We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset S of a reference domain, and the complement of S is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure S , which is the total work of the pressure and internal forces at the equilibrium displacement. In order to prevent from homogenization we add a penalization on the perimeter of S . We propose an approximation of our problem in the framework of Γ -convergence, based on an approximation of our three phases by a smooth phase-field. We detail the numerical implementation of the approximate energies and show a few experiments.

How to cite

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Bourdin, Blaise, and Chambolle, Antonin. "Design-dependent loads in topology optimization." ESAIM: Control, Optimisation and Calculus of Variations 9 (2003): 19-48. <http://eudml.org/doc/245317>.

@article{Bourdin2003,
abstract = {We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset $S$ of a reference domain, and the complement of $S$ is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure $S$, which is the total work of the pressure and internal forces at the equilibrium displacement. In order to prevent from homogenization we add a penalization on the perimeter of $S$. We propose an approximation of our problem in the framework of $\Gamma $-convergence, based on an approximation of our three phases by a smooth phase-field. We detail the numerical implementation of the approximate energies and show a few experiments.},
author = {Bourdin, Blaise, Chambolle, Antonin},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {topology optimization; optimal design; design-dependent loads; $\Gamma $-convergence; diffuse interface method; Gamma-convergence},
language = {eng},
pages = {19-48},
publisher = {EDP-Sciences},
title = {Design-dependent loads in topology optimization},
url = {http://eudml.org/doc/245317},
volume = {9},
year = {2003},
}

TY - JOUR
AU - Bourdin, Blaise
AU - Chambolle, Antonin
TI - Design-dependent loads in topology optimization
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2003
PB - EDP-Sciences
VL - 9
SP - 19
EP - 48
AB - We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset $S$ of a reference domain, and the complement of $S$ is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure $S$, which is the total work of the pressure and internal forces at the equilibrium displacement. In order to prevent from homogenization we add a penalization on the perimeter of $S$. We propose an approximation of our problem in the framework of $\Gamma $-convergence, based on an approximation of our three phases by a smooth phase-field. We detail the numerical implementation of the approximate energies and show a few experiments.
LA - eng
KW - topology optimization; optimal design; design-dependent loads; $\Gamma $-convergence; diffuse interface method; Gamma-convergence
UR - http://eudml.org/doc/245317
ER -

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Citations in EuDML Documents

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  1. Elie Bretin, Valerie Perrier, Phase field method for mean curvature flow with boundary constraints
  2. Patrick Penzler, Martin Rumpf, Benedikt Wirth, A phase-field model for compliance shape optimization in nonlinear elasticity
  3. Patrick Penzler, Martin Rumpf, Benedikt Wirth, A phase-field model for compliance shape optimization in nonlinear elasticity
  4. Elie Bretin, Valerie Perrier, Phase field method for mean curvature flow with boundary constraints
  5. Patrick Penzler, Martin Rumpf, Benedikt Wirth, A phase-field model for compliance shape optimization in nonlinear elasticity
  6. Luise Blank, Harald Garcke, M. Hassan Farshbaf-Shaker, Vanessa Styles, Relating phase field and sharp interface approaches to structural topology optimization

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