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Title: Stiffness optimization of non-linear elastic structures

Abstract

Our 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. And 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. We formulate a well-posed topology optimization problem 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.

Authors:
 [1];  [1];  [2]
+ Show Author Affiliations
  1. Lund Univ. (Sweden). Division of Solid Mechanics
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Design and Optimization
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1416502
Alternate Identifier(s):
OSTI ID: 1549081
Report Number(s):
LLNL-JRNL-731767
Journal ID: ISSN 0045-7825; TRN: US1800942
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 330; Journal Issue: C; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; topology optimization; stiffness optimization; finite strains; non-linear elasticity

Citation Formats

Wallin, Mathias, Ivarsson, Niklas, and Tortorelli, Daniel. Stiffness optimization of non-linear elastic structures. United States: N. p., 2017. Web. doi:10.1016/j.cma.2017.11.004.
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Wallin, Mathias, Ivarsson, Niklas, & Tortorelli, Daniel. Stiffness optimization of non-linear elastic structures. United States. https://doi.org/10.1016/j.cma.2017.11.004
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Wallin, Mathias, Ivarsson, Niklas, and Tortorelli, Daniel. Mon . "Stiffness optimization of non-linear elastic structures". United States. https://doi.org/10.1016/j.cma.2017.11.004. https://www.osti.gov/servlets/purl/1416502.
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@article{osti_1416502,
title = {Stiffness optimization of non-linear elastic structures},
author = {Wallin, Mathias and Ivarsson, Niklas and Tortorelli, Daniel},
abstractNote = {Our 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. And 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. We formulate a well-posed topology optimization problem 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.},
doi = {10.1016/j.cma.2017.11.004},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 330,
place = {United States},
year = {Mon Nov 13 00:00:00 EST 2017},
month = {Mon Nov 13 00:00:00 EST 2017}
}
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https://doi.org/10.1016/j.cma.2017.11.004
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Works referenced in this record:

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    Works referencing / citing this record:

    Topology optimization of finite strain viscoplastic systems under transient loads: Transient finite strain viscoplastic effects in topology optimization
    journal, March 2018

    • Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel
    • International Journal for Numerical Methods in Engineering, Vol. 114, Issue 13
    • DOI: 10.1002/nme.5789

    A 213-line topology optimization code for geometrically nonlinear structures
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    • Structural and Multidisciplinary Optimization, Vol. 59, Issue 5
    • DOI: 10.1007/s00158-018-2138-5

    Distortion energy-based topology optimization design of hyperelastic materials
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    • Structural and Multidisciplinary Optimization, Vol. 59, Issue 6
    • DOI: 10.1007/s00158-018-2161-6

    Shape preserving design of geometrically nonlinear structures using topology optimization
    journal, January 2019

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    • Structural and Multidisciplinary Optimization, Vol. 59, Issue 4
    • DOI: 10.1007/s00158-018-2186-x

    Computational shape optimisation for a gradient-enhanced continuum damage model
    journal, January 2020

    Computational shape optimisation for a gradient-enhanced continuum damage model
    text, January 2020

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