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
- 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... (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:
https://lup.lub.lu.se/record/3164174
- author
- Wallin, Mathias
LU
and Ristinmaa, Matti
LU
- organization
- publishing date
- 2013
- 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 Inc.
- 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
- 2016-04-01 10:53:03
- date last changed
- 2022-03-20 00:59:10
@article{3d86a7ca-5653-49f0-8a6a-f87431235ff3,
abstract = {{Abstract in Undetermined<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}},
keywords = {{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 Inc.}},
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}},
doi = {{10.1002/nme.4434}},
volume = {{94}},
year = {{2013}},
}