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Finite strain topology optimization based on phase-field regularization

Wallin, Mathias LU and Ristinmaa, Matti LU (2014) In Structural and Multidisciplinary Optimization 51(2). p.305-317
Abstract

In this paper the topology optimization problem is solved in a finite strain setting using a polyconvex hyperelastic material. Since finite strains is considered the definition of the stiffness is not unique. In the present contribution, the objective of the optimization is minimization of the end-displacement for a given amount of material. The problem is regularized using the phase-field approach which leads to that the optimality criterion is defined by a second order partial differential equation. Both the elastic boundary value problem and the optimality criterion is solved using the finite element method. To approach the optimal state a steepest descent approach is utilized. The interfaces between void and full material are... (More)

In this paper the topology optimization problem is solved in a finite strain setting using a polyconvex hyperelastic material. Since finite strains is considered the definition of the stiffness is not unique. In the present contribution, the objective of the optimization is minimization of the end-displacement for a given amount of material. The problem is regularized using the phase-field approach which leads to that the optimality criterion is defined by a second order partial differential equation. Both the elastic boundary value problem and the optimality criterion is solved using the finite element method. To approach the optimal state a steepest descent approach is utilized. The interfaces between void and full material are resolved using an adaptive finite element scheme. The paper is closed by numerical examples that clearly illustrates that the presented method is able to find optimal solutions for finite strain topology optimization problems. © 2014 Springer-Verlag Berlin Heidelberg.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Finite strain, Phase field, Topology optimization
in
Structural and Multidisciplinary Optimization
volume
51
issue
2
pages
305 - 317
publisher
Springer
external identifiers
  • scopus:84906035169
  • scopus:85027943711
ISSN
1615-147X
DOI
10.1007/s00158-014-1141-8
language
English
LU publication?
yes
id
30a5f547-017e-4999-8716-dd59255fb9e8
date added to LUP
2016-09-01 21:24:19
date last changed
2017-10-01 05:22:55
@article{30a5f547-017e-4999-8716-dd59255fb9e8,
  abstract     = {<p>In this paper the topology optimization problem is solved in a finite strain setting using a polyconvex hyperelastic material. Since finite strains is considered the definition of the stiffness is not unique. In the present contribution, the objective of the optimization is minimization of the end-displacement for a given amount of material. The problem is regularized using the phase-field approach which leads to that the optimality criterion is defined by a second order partial differential equation. Both the elastic boundary value problem and the optimality criterion is solved using the finite element method. To approach the optimal state a steepest descent approach is utilized. The interfaces between void and full material are resolved using an adaptive finite element scheme. The paper is closed by numerical examples that clearly illustrates that the presented method is able to find optimal solutions for finite strain topology optimization problems. © 2014 Springer-Verlag Berlin Heidelberg.</p>},
  author       = {Wallin, Mathias and Ristinmaa, Matti},
  issn         = {1615-147X},
  keyword      = {Finite strain,Phase field,Topology optimization},
  language     = {eng},
  month        = {08},
  number       = {2},
  pages        = {305--317},
  publisher    = {Springer},
  series       = {Structural and Multidisciplinary Optimization},
  title        = {Finite strain topology optimization based on phase-field regularization},
  url          = {http://dx.doi.org/10.1007/s00158-014-1141-8},
  volume       = {51},
  year         = {2014},
}