Stiffness optimization of non-linear elastic structures

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

doi:10.1016/j.cma.2017.11.004

Stiffness optimization of non-linear elastic structures

Journal Article · Mon Nov 13 00:00:00 EST 2017 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2017.11.004· OSTI ID:1416502

Wallin, Mathias ^[1]; Ivarsson, Niklas ^[1]; Tortorelli, Daniel ^[2]

Lund Univ. (Sweden). Division of Solid Mechanics
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Design and Optimization

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.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1416502

Alternate ID(s):: OSTI ID: 1549081

Report Number(s):: LLNL-JRNL--731767

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 330; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (17)

Achieving minimum length scale in topology optimization using nodal design variables and projection functions Guest, J. K.; Prévost, J. H.; Belytschko, T. International Journal for Numerical Methods in Engineering, Vol. 61, Issue 2 https://doi.org/10.1002/nme.1064	journal	August 2004
The method of moving asymptotes—a new method for structural optimization Svanberg, Krister International Journal for Numerical Methods in Engineering, Vol. 24, Issue 2 https://doi.org/10.1002/nme.1620240207	journal	February 1987
Filters in topology optimization based on Helmholtz-type differential equations Lazarov, B. S.; Sigmund, O. International Journal for Numerical Methods in Engineering, Vol. 86, Issue 6 https://doi.org/10.1002/nme.3072	journal	December 2010
Large strain phase-field-based multi-material topology optimization: Large Strain Phase-Field-Based Multi-Material Topology Optimization Wallin, Mathias; Ivarsson, Niklas; Ristinmaa, Matti International Journal for Numerical Methods in Engineering, Vol. 104, Issue 9 https://doi.org/10.1002/nme.4962	journal	June 2015
An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms Bruns, T. E.; Tortorelli, D. A. International Journal for Numerical Methods in Engineering, Vol. 57, Issue 10 https://doi.org/10.1002/nme.783	journal	January 2003
Optimal shape design as a material distribution problem Bendsøe, M. P. Structural Optimization, Vol. 1, Issue 4 https://doi.org/10.1007/BF01650949	journal	December 1989
Large deformations and stability in topology optimization Kemmler, R.; Lipka, A.; Ramm, E. Structural and Multidisciplinary Optimization, Vol. 30, Issue 6 https://doi.org/10.1007/s00158-005-0534-0	journal	July 2005
Stress-based topology optimization for continua Le, Chau; Norato, Julian; Bruns, Tyler Structural and Multidisciplinary Optimization, Vol. 41, Issue 4 https://doi.org/10.1007/s00158-009-0440-y	journal	October 2009
Heaviside projection based topology optimization by a PDE-filtered scalar function Kawamoto, Atsushi; Matsumori, Tadayoshi; Yamasaki, Shintaro Structural and Multidisciplinary Optimization, Vol. 44, Issue 1 https://doi.org/10.1007/s00158-010-0562-2	journal	August 2010
On projection methods, convergence and robust formulations in topology optimization Wang, Fengwen; Lazarov, Boyan Stefanov; Sigmund, Ole Structural and Multidisciplinary Optimization, Vol. 43, Issue 6 https://doi.org/10.1007/s00158-010-0602-y	journal	December 2010
Topology optimization of hyperelastic bodies including non-zero prescribed displacements Klarbring, Anders; Strömberg, Niclas Structural and Multidisciplinary Optimization, Vol. 47, Issue 1 https://doi.org/10.1007/s00158-012-0819-z	journal	June 2012
Topology optimization approaches: A comparative review Sigmund, Ole; Maute, Kurt Structural and Multidisciplinary Optimization, Vol. 48, Issue 6 https://doi.org/10.1007/s00158-013-0978-6	journal	August 2013
Stiffness design of geometrically nonlinear structures using topology optimization Buhl, T.; Pedersen, C. B. W.; Sigmund, O. Structural and Multidisciplinary Optimization, Vol. 19, Issue 2 https://doi.org/10.1007/s001580050089	journal	April 2000
Topology optimization of non-linear elastic structures and compliant mechanisms Bruns, Tyler E.; Tortorelli, Daniel A. Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 26-27 https://doi.org/10.1016/S0045-7825(00)00278-4	journal	March 2001
Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems Wang, Fengwen; Lazarov, Boyan Stefanov; Sigmund, Ole Computer Methods in Applied Mechanics and Engineering, Vol. 276 https://doi.org/10.1016/j.cma.2014.03.021	journal	July 2014
Combination of topology optimization and optimal control method Deng, Yongbo; Liu, Zhenyu; Liu, Yongshun Journal of Computational Physics, Vol. 257 https://doi.org/10.1016/j.jcp.2013.09.033	journal	January 2014
Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method Deng, Yongbo; Korvink, Jan G. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 472, Issue 2189 https://doi.org/10.1098/rspa.2015.0835	journal	May 2016

Cited By (6)

Topology optimization of finite strain viscoplastic systems under transient loads: Transient finite strain viscoplastic effects in topology optimization Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel International Journal for Numerical Methods in Engineering, Vol. 114, Issue 13 https://doi.org/10.1002/nme.5789	journal	March 2018
A 213-line topology optimization code for geometrically nonlinear structures Chen, Qi; Zhang, Xianmin; Zhu, Benliang Structural and Multidisciplinary Optimization, Vol. 59, Issue 5 https://doi.org/10.1007/s00158-018-2138-5	journal	November 2018
Distortion energy-based topology optimization design of hyperelastic materials Deng, Hao; Cheng, Lin; C. To, Albert Structural and Multidisciplinary Optimization, Vol. 59, Issue 6 https://doi.org/10.1007/s00158-018-2161-6	journal	December 2018
Shape preserving design of geometrically nonlinear structures using topology optimization Li, Yu; Zhu, Jihong; Wang, Fengwen Structural and Multidisciplinary Optimization, Vol. 59, Issue 4 https://doi.org/10.1007/s00158-018-2186-x	journal	January 2019
Computational shape optimisation for a gradient-enhanced continuum damage model Guhr, Fabian; Sprave, Leon; Barthold, Franz-Joseph Computational Mechanics, Vol. 65, Issue 4 https://doi.org/10.1007/s00466-019-01810-3	journal	January 2020
Computational shape optimisation for a gradient-enhanced continuum damage model Guhr, Fabian; Sprave, Leon; Barthold, Franz-Joseph TU Dortmund https://doi.org/10.17877/de290r-22145	text	January 2020

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Stiffness optimization of non-linear elastic structures

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