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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 of a reference domain, and the complement of 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 , 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 . We propose an approximation of our problem in the framework of -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.
Keywords: topology optimization, optimal design, design-dependent loads, $\Gamma $-convergence, diffuse interface method
@article{COCV_2003__9__19_0,
author = {Bourdin, Blaise and Chambolle, Antonin},
title = {Design-dependent loads in topology optimization},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {19--48},
publisher = {EDP-Sciences},
volume = {9},
year = {2003},
doi = {10.1051/cocv:2002070},
mrnumber = {1957089},
zbl = {1066.49029},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002070/}
}
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 SP - 19 EP - 48 VL - 9 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002070/ DO - 10.1051/cocv:2002070 LA - en ID - COCV_2003__9__19_0 ER -
%0 Journal Article %A Bourdin, Blaise %A Chambolle, Antonin %T Design-dependent loads in topology optimization %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 19-48 %V 9 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002070/ %R 10.1051/cocv:2002070 %G en %F COCV_2003__9__19_0
Bourdin, Blaise; Chambolle, Antonin. Design-dependent loads in topology optimization. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 19-48. doi: 10.1051/cocv:2002070
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