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Boundary Effects in a Phase-Field approach to Topology Optimization

Wallin, Mathias LU and Ristinmaa, Matti LU (2014) In Computer Methods in Applied Mechanics and Engineering 278. p.145-159
Abstract
A phase-field based topology optimization approach is considered for the maximum stiffness or minimum compliance problem. The objective functional to be minimized consists in addition to the compliance a cost for gray solutions and a cost for interfaces between void and full material. Since the interfaces between void and full material are penalized via a volume integral in the original phase-field formulation there is no penalty associated with interfaces along the external boundaries. In the present contribution, an additional term representing the cost of interfaces at external boundaries is added to the functional subject to minimization. It is shown that the new boundary term enters the optimization as a Robin boundary condition. The... (More)
A phase-field based topology optimization approach is considered for the maximum stiffness or minimum compliance problem. The objective functional to be minimized consists in addition to the compliance a cost for gray solutions and a cost for interfaces between void and full material. Since the interfaces between void and full material are penalized via a volume integral in the original phase-field formulation there is no penalty associated with interfaces along the external boundaries. In the present contribution, an additional term representing the cost of interfaces at external boundaries is added to the functional subject to minimization. It is shown that the new boundary term enters the optimization as a Robin boundary condition. The method is implemented in a finite element setting and numerical simulations of typical structures are considered. The results indicate that the optimal designs are influenced by the cost of interfaces to a large (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Topology optimization, Phase-field, Boundary energy, Double obstacle problem, Howard’s algorithm
in
Computer Methods in Applied Mechanics and Engineering
volume
278
pages
145 - 159
publisher
Elsevier
external identifiers
  • wos:000340301200008
  • scopus:84944865558
ISSN
0045-7825
DOI
10.1016/j.cma.2014.05.012
language
English
LU publication?
yes
id
ed05483f-8cea-4eca-b6eb-3e0e142c5907 (old id 4466211)
date added to LUP
2014-06-19 11:14:08
date last changed
2017-10-29 03:53:34
@article{ed05483f-8cea-4eca-b6eb-3e0e142c5907,
  abstract     = {A phase-field based topology optimization approach is considered for the maximum stiffness or minimum compliance problem. The objective functional to be minimized consists in addition to the compliance a cost for gray solutions and a cost for interfaces between void and full material. Since the interfaces between void and full material are penalized via a volume integral in the original phase-field formulation there is no penalty associated with interfaces along the external boundaries. In the present contribution, an additional term representing the cost of interfaces at external boundaries is added to the functional subject to minimization. It is shown that the new boundary term enters the optimization as a Robin boundary condition. The method is implemented in a finite element setting and numerical simulations of typical structures are considered. The results indicate that the optimal designs are influenced by the cost of interfaces to a large},
  author       = {Wallin, Mathias and Ristinmaa, Matti},
  issn         = {0045-7825},
  keyword      = {Topology optimization,Phase-field,Boundary energy,Double obstacle problem,Howard’s algorithm},
  language     = {eng},
  pages        = {145--159},
  publisher    = {Elsevier},
  series       = {Computer Methods in Applied Mechanics and Engineering},
  title        = {Boundary Effects in a Phase-Field approach to Topology Optimization},
  url          = {http://dx.doi.org/10.1016/j.cma.2014.05.012},
  volume       = {278},
  year         = {2014},
}