# 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

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topBourdin, 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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- Patrick Penzler, Martin Rumpf, Benedikt Wirth, A phase-field model for compliance shape optimization in nonlinear elasticity
- 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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