# Relating phase field and sharp interface approaches to structural topology optimization

Luise Blank; Harald Garcke; M. Hassan Farshbaf-Shaker; Vanessa Styles

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 4, page 1025-1058
- ISSN: 1292-8119

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topBlank, Luise, et al. "Relating phase field and sharp interface approaches to structural topology optimization." ESAIM: Control, Optimisation and Calculus of Variations 20.4 (2014): 1025-1058. <http://eudml.org/doc/272854>.

@article{Blank2014,

abstract = {A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.},

author = {Blank, Luise, Garcke, Harald, Hassan Farshbaf-Shaker, M., Styles, Vanessa},

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

keywords = {structural topology optimization; linear elasticity; phase-field method; first order conditions; matched asymptotic expansions; shape calculus; numerical simulations; first order optimality conditions},

language = {eng},

number = {4},

pages = {1025-1058},

publisher = {EDP-Sciences},

title = {Relating phase field and sharp interface approaches to structural topology optimization},

url = {http://eudml.org/doc/272854},

volume = {20},

year = {2014},

}

TY - JOUR

AU - Blank, Luise

AU - Garcke, Harald

AU - Hassan Farshbaf-Shaker, M.

AU - Styles, Vanessa

TI - Relating phase field and sharp interface approaches to structural topology optimization

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2014

PB - EDP-Sciences

VL - 20

IS - 4

SP - 1025

EP - 1058

AB - A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.

LA - eng

KW - structural topology optimization; linear elasticity; phase-field method; first order conditions; matched asymptotic expansions; shape calculus; numerical simulations; first order optimality conditions

UR - http://eudml.org/doc/272854

ER -

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