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Howard's algorithm in a phase-field topology optimization approach

Wallin, Mathias LU and Ristinmaa, Matti LU (2013) In International Journal for Numerical Methods in Engineering 94(1). p.43-59
Abstract (Swedish)
Abstract in Undetermined

The topology optimization problem is formulated in a phase-field approach. The solution procedure is based on the Allan–Cahn diffusion model where the conservation of volume is enforced by a global constraint. The functional defining the minimization problem is selected such that no penalization is imposed for full and void materials. Upper and lower bounds of the density function are enforced by infinite penalty at the bounds. A gradient term that introduces cost for boundaries and thereby regularizing the problem is also included in the objective functional. Conditions for stationarity of the functional are derived, and it is shown that the problem can be stated as a variational inequality or a... (More)
Abstract in Undetermined

The topology optimization problem is formulated in a phase-field approach. The solution procedure is based on the Allan–Cahn diffusion model where the conservation of volume is enforced by a global constraint. The functional defining the minimization problem is selected such that no penalization is imposed for full and void materials. Upper and lower bounds of the density function are enforced by infinite penalty at the bounds. A gradient term that introduces cost for boundaries and thereby regularizing the problem is also included in the objective functional. Conditions for stationarity of the functional are derived, and it is shown that the problem can be stated as a variational inequality or a max–min problem, both defining a double obstacle problem. The numerical examples used to demonstrate the method are solved using the FEM, whereas the double obstacle problem is solved using Howard's algorithm. (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
barrier functions, phase-field, topology optimization, double obstacle problems, variational inequality, Howard's algorithm
in
International Journal for Numerical Methods in Engineering
volume
94
issue
1
pages
43 - 59
publisher
John Wiley & Sons
external identifiers
  • wos:000316691500003
  • scopus:84875616507
ISSN
1097-0207
DOI
10.1002/nme.4434
language
English
LU publication?
yes
id
3d86a7ca-5653-49f0-8a6a-f87431235ff3 (old id 3164174)
date added to LUP
2012-11-12 16:26:29
date last changed
2019-02-20 02:51:28
@article{3d86a7ca-5653-49f0-8a6a-f87431235ff3,
  abstract     = {<b>Abstract in Undetermined</b><br/><br>
The topology optimization problem is formulated in a phase-field approach. The solution procedure is based on the Allan–Cahn diffusion model where the conservation of volume is enforced by a global constraint. The functional defining the minimization problem is selected such that no penalization is imposed for full and void materials. Upper and lower bounds of the density function are enforced by infinite penalty at the bounds. A gradient term that introduces cost for boundaries and thereby regularizing the problem is also included in the objective functional. Conditions for stationarity of the functional are derived, and it is shown that the problem can be stated as a variational inequality or a max–min problem, both defining a double obstacle problem. The numerical examples used to demonstrate the method are solved using the FEM, whereas the double obstacle problem is solved using Howard's algorithm.},
  author       = {Wallin, Mathias and Ristinmaa, Matti},
  issn         = {1097-0207},
  keyword      = {barrier functions,phase-field,topology optimization,double obstacle problems,variational inequality,Howard's algorithm},
  language     = {eng},
  number       = {1},
  pages        = {43--59},
  publisher    = {John Wiley & Sons},
  series       = {International Journal for Numerical Methods in Engineering},
  title        = {Howard's algorithm in a phase-field topology optimization approach},
  url          = {http://dx.doi.org/10.1002/nme.4434},
  volume       = {94},
  year         = {2013},
}