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.

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}, zbl = {1066.49029}, mrnumber = {1957089}, language = {en}, url = {http://www.numdam.org/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 DA - 2003/// SP - 19 EP - 48 VL - 9 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2002070/ UR - https://zbmath.org/?q=an%3A1066.49029 UR - https://www.ams.org/mathscinet-getitem?mr=1957089 UR - https://doi.org/10.1051/cocv:2002070 DO - 10.1051/cocv:2002070 LA - en ID - COCV_2003__9__19_0 ER -

Bourdin, Blaise; Chambolle, Antonin. Design-dependent loads in topology optimization. ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 19-48. doi : 10.1051/cocv:2002070. http://www.numdam.org/articles/10.1051/cocv:2002070/

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