Stiffness optimization of nonlinear elastic structures
Our paper revisits stiffness optimization of nonlinear elastic structures. Due to the nonlinearity, 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 wellposed 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:

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 Lund Univ. (Sweden). Division of Solid Mechanics
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Design and Optimization
 Publication Date:
 Report Number(s):
 LLNLJRNL731767
Journal ID: ISSN 00457825; TRN: US1800942
 Grant/Contract Number:
 AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 Computer Methods in Applied Mechanics and Engineering
 Additional Journal Information:
 Journal Volume: 330; Journal Issue: C; Journal ID: ISSN 00457825
 Publisher:
 Elsevier
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING; topology optimization; stiffness optimization; finite strains; nonlinear elasticity
 OSTI Identifier:
 1416502
Wallin, Mathias, Ivarsson, Niklas, and Tortorelli, Daniel. Stiffness optimization of nonlinear elastic structures. United States: N. p.,
Web. doi:10.1016/j.cma.2017.11.004.
Wallin, Mathias, Ivarsson, Niklas, & Tortorelli, Daniel. Stiffness optimization of nonlinear elastic structures. United States. doi:10.1016/j.cma.2017.11.004.
Wallin, Mathias, Ivarsson, Niklas, and Tortorelli, Daniel. 2017.
"Stiffness optimization of nonlinear elastic structures". United States.
doi:10.1016/j.cma.2017.11.004.
@article{osti_1416502,
title = {Stiffness optimization of nonlinear elastic structures},
author = {Wallin, Mathias and Ivarsson, Niklas and Tortorelli, Daniel},
abstractNote = {Our paper revisits stiffness optimization of nonlinear elastic structures. Due to the nonlinearity, 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 wellposed 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 = {2017},
month = {11}
}