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Stiffness optimization of non-linear elastic structures

Wallin, Mathias LU ; Ivarsson, Niklas LU and Tortorelli, Daniel (2018) In Computer Methods in Applied Mechanics and Engineering 330. p.292-307
Abstract

This paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. For the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed by using a fictitious strain energy such that small strain linear... (More)

This paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. For the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed by using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. A well posed topology optimization problem is formulated by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Finite strains, Non-linear elasticity, Stiffness optimization, Topology optimization
in
Computer Methods in Applied Mechanics and Engineering
volume
330
pages
16 pages
publisher
Elsevier
external identifiers
  • scopus:85034860957
ISSN
0045-7825
DOI
language
English
LU publication?
yes
id
5a244785-6287-4272-81af-c8683da53e0e
date added to LUP
2017-12-07 09:56:33
date last changed
2018-06-17 05:28:51
@article{5a244785-6287-4272-81af-c8683da53e0e,
  abstract     = {<p>This paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. For the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed by using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. A well posed topology optimization problem is formulated by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.</p>},
  author       = {Wallin, Mathias and Ivarsson, Niklas and Tortorelli, Daniel},
  issn         = {0045-7825},
  keyword      = {Finite strains,Non-linear elasticity,Stiffness optimization,Topology optimization},
  language     = {eng},
  month        = {03},
  pages        = {292--307},
  publisher    = {Elsevier},
  series       = {Computer Methods in Applied Mechanics and Engineering},
  title        = {Stiffness optimization of non-linear elastic structures},
  url          = {http://dx.doi.org/},
  volume       = {330},
  year         = {2018},
}