# Design-dependent loads in topology optimization

Blaise Bourdin; Antonin Chambolle

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- 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 (2010): 19-48. <http://eudml.org/doc/90690>.

@article{Bourdin2010,

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
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.
},

author = {Bourdin, Blaise, Chambolle, Antonin},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Topology optimization; optimal design; design-dependent
loads; Γ-convergence; diffuse interface method.; topology optimization; design-dependent loads; Gamma-convergence; diffuse interface method},

language = {eng},

month = {3},

pages = {19-48},

publisher = {EDP Sciences},

title = {Design-dependent loads in topology optimization},

url = {http://eudml.org/doc/90690},

volume = {9},

year = {2010},

}

TY - JOUR

AU - Bourdin, Blaise

AU - Chambolle, Antonin

TI - Design-dependent loads in topology optimization

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

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
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.

LA - eng

KW - Topology optimization; optimal design; design-dependent
loads; Γ-convergence; diffuse interface method.; topology optimization; design-dependent loads; Gamma-convergence; diffuse interface method

UR - http://eudml.org/doc/90690

ER -

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