Achieving stress-constrained topological design via length scale control

Amir, Oded; Lazarov, Boyan S.

doi:10.1007/s00158-018-2019-y

Title: Achieving stress-constrained topological design via length scale control

Journal Article · 07 June 2018 · Structural and Multidisciplinary Optimization

DOI: https://doi.org/10.1007/s00158-018-2019-y · OSTI ID:1809154

^[1]; Lazarov, Boyan S. ^[2]

Technion-Israel Institute of Technology, Haifa (Israel). Faculty of Civil and Environmental Engineering
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Univ. of Manchester (United Kingdom). School of Mechanical, Aerospace and Civil Engineering

A new suite of computational procedures for stress-constrained continuum topology optimization is presented. In contrast to common approaches for imposing stress constraints, herein it is proposed to limit the maximum stress by controlling the length scale of the optimized design. Several procedures are formulated based on the treatment of the filter radius as a design variable. This enables to automatically manipulate the minimum length scale such that stresses are constrained to the allowable value, while the optimization is driven to minimizing compliance under a volume constraint – without any direct constraints on stresses. Numerical experiments are presented that incorporate the following : 1) Global control over the filter radius that leads to a uniform minimum length scale throughout the design; 2) Spatial variation of the filter radius that leads to local manipulation of the minimum length according to stress concentrations; and 3) Combinations of the two above. The optimized designs provide high-quality trade-offs between compliance, stress and volume. From a computational perspective, the proposed procedures are efficient and simple to implement: essentially, stress-constrained topology optimization is posed as a minimum compliance problem with additional treatment of the length scale.

View Accepted Manuscript (DOE)

Cite

Export

Save

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

Sponsoring Organization:: Israeli Science Foundation; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1809154

Report Number(s):: LLNL-JRNL--744100; 899076

Journal Information:: Structural and Multidisciplinary Optimization, Journal Name: Structural and Multidisciplinary Optimization Journal Issue: 5 Vol. 58; ISSN 1615-147X

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (48)

Topology optimization of continuum structures with local stress constraints Duysinx, P.; Bendsøe, M. P. International Journal for Numerical Methods in Engineering, Vol. 43, Issue 8 https://doi.org/10.1002/(SICI)1097-0207(19981230)43:8<1453::AID-NME480>3.0.CO;2-2	journal	December 1998
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
Filters in topology optimization Bourdin, Blaise International Journal for Numerical Methods in Engineering, Vol. 50, Issue 9 https://doi.org/10.1002/nme.116	journal	January 2001
Bilateral filtering for structural topology optimization Wang, Michael Yu; Wang, Shengyin International Journal for Numerical Methods in Engineering, Vol. 63, Issue 13 https://doi.org/10.1002/nme.1347	journal	January 2005
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
A mixed FEM approach to stress-constrained topology optimization Bruggi, M.; Venini, P. International Journal for Numerical Methods in Engineering, Vol. 73, Issue 12 https://doi.org/10.1002/nme.2138	journal	January 2008
A new scheme for imposing a minimum length scale in topology optimization Poulsen, Thomas A. International Journal for Numerical Methods in Engineering, Vol. 57, Issue 6 https://doi.org/10.1002/nme.694	journal	January 2003
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
Topology Optimization with Stress Constraints Using Isotropic Damage with Strain Softening Zelickman, Yakov; Amir, Oded Advances in Structural and Multidisciplinary Optimization https://doi.org/10.1007/978-3-319-67988-4_75	book	December 2017
Topology and Generalized Layout Optimization of Elastic Structures Bendsøe, Martin Philip; Díaz, Alejandro; Kikuchi, Noboru Topology Design of Structures https://doi.org/10.1007/978-94-011-1804-0_13	book	January 1993
Stress-based topology optimization Yang, R. J.; Chen, C. J. Structural Optimization, Vol. 12, Issue 2-3 https://doi.org/10.1007/BF01196941	journal	October 1996
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
Topology optimization of continuum structures with material failure constraints Pereira, J. T.; Fancello, E. A.; Barcellos, C. S. Structural and Multidisciplinary Optimization, Vol. 26, Issue 1-2 https://doi.org/10.1007/s00158-003-0301-z	journal	January 2004
Topology optimization for minimum mass design considering local failure constraints and contact boundary conditions Fancello, E. A. Structural and Multidisciplinary Optimization, Vol. 32, Issue 3 https://doi.org/10.1007/s00158-006-0019-9	journal	July 2006
Morphology-based black and white filters for topology optimization Sigmund, Ole Structural and Multidisciplinary Optimization, Vol. 33, Issue 4-5 https://doi.org/10.1007/s00158-006-0087-x	journal	January 2007
Topological optimization of structures subject to Von Mises stress constraints Amstutz, Samuel; Novotny, Antonio A. Structural and Multidisciplinary Optimization, Vol. 41, Issue 3 https://doi.org/10.1007/s00158-009-0425-x	journal	August 2009
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
Volume preserving nonlinear density filter based on heaviside functions Xu, Shengli; Cai, Yuanwu; Cheng, Gengdong Structural and Multidisciplinary Optimization, Vol. 41, Issue 4 https://doi.org/10.1007/s00158-009-0452-7	journal	December 2009
Efficient topology optimization in MATLAB using 88 lines of code Andreassen, Erik; Clausen, Anders; Schevenels, Mattias Structural and Multidisciplinary Optimization, Vol. 43, Issue 1 https://doi.org/10.1007/s00158-010-0594-7	journal	November 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 for minimum weight with compliance and stress constraints Bruggi, Matteo; Duysinx, Pierre Structural and Multidisciplinary Optimization, Vol. 46, Issue 3 https://doi.org/10.1007/s00158-012-0759-7	journal	January 2012
Stress constrained topology optimization Holmberg, Erik; Torstenfelt, Bo; Klarbring, Anders Structural and Multidisciplinary Optimization, Vol. 48, Issue 1 https://doi.org/10.1007/s00158-012-0880-7	journal	February 2013
A survey of structural and multidisciplinary continuum topology optimization: post 2000 Deaton, Joshua D.; Grandhi, Ramana V. Structural and Multidisciplinary Optimization, Vol. 49, Issue 1 https://doi.org/10.1007/s00158-013-0956-z	journal	July 2013
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
Stress-constrained topology optimization for compliant mechanism design De Leon, Daniel M.; Alexandersen, Joe; O. Fonseca, Jun S. Structural and Multidisciplinary Optimization, Vol. 52, Issue 5 https://doi.org/10.1007/s00158-015-1279-z	journal	July 2015
Damage approach: A new method for topology optimization with local stress constraints Verbart, Alexander; Langelaar, Matthijs; Keulen, Fred van Structural and Multidisciplinary Optimization, Vol. 53, Issue 5 https://doi.org/10.1007/s00158-015-1318-9	journal	December 2015
A unified aggregation and relaxation approach for stress-constrained topology optimization Verbart, Alexander; Langelaar, Matthijs; Keulen, Fred van Structural and Multidisciplinary Optimization, Vol. 55, Issue 2 https://doi.org/10.1007/s00158-016-1524-0	journal	July 2016
Stress-constrained continuum topology optimization: a new approach based on elasto-plasticity Amir, Oded Structural and Multidisciplinary Optimization, Vol. 55, Issue 5 https://doi.org/10.1007/s00158-016-1618-8	journal	November 2016
Combined shape and topology optimization for minimization of maximal von Mises stress Lian, Haojie; Christiansen, Asger N.; Tortorelli, Daniel A. Structural and Multidisciplinary Optimization, Vol. 55, Issue 5 https://doi.org/10.1007/s00158-017-1656-x	journal	January 2017
Topology optimization with finite-life fatigue constraints Oest, Jacob; Lund, Erik Structural and Multidisciplinary Optimization, Vol. 56, Issue 5 https://doi.org/10.1007/s00158-017-1701-9	journal	June 2017
On filter boundary conditions in topology optimization Clausen, Anders; Andreassen, Erik Structural and Multidisciplinary Optimization, Vol. 56, Issue 5 https://doi.org/10.1007/s00158-017-1709-1	journal	June 2017
On fully stressed design and p-norm measures in structural optimization Zhou, Mingdong; Sigmund, Ole Structural and Multidisciplinary Optimization, Vol. 56, Issue 3 https://doi.org/10.1007/s00158-017-1731-3	journal	June 2017
Stress-based topology optimization using spatial gradient stabilized XFEM Sharma, Ashesh; Maute, Kurt Structural and Multidisciplinary Optimization, Vol. 57, Issue 1 https://doi.org/10.1007/s00158-017-1833-y	journal	October 2017
A 99 line topology optimization code written in Matlab Sigmund, O. Structural and Multidisciplinary Optimization, Vol. 21, Issue 2 https://doi.org/10.1007/s001580050176	journal	April 2001
Length scale and manufacturability in density-based topology optimization Lazarov, Boyan S.; Wang, Fengwen; Sigmund, Ole Archive of Applied Mechanics, Vol. 86, Issue 1-2 https://doi.org/10.1007/s00419-015-1106-4	journal	January 2016
Design of materials with extreme thermal expansion using a three-phase topology optimization method Sigmund, O.; Torquato, S. Journal of the Mechanics and Physics of Solids, Vol. 45, Issue 6 https://doi.org/10.1016/S0022-5096(96)00114-7	journal	June 1997
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
Block aggregation of stress constraints in topology optimization of structures París, J.; Navarrina, F.; Colominas, I. Advances in Engineering Software, Vol. 41, Issue 3 https://doi.org/10.1016/j.advengsoft.2009.03.006	journal	March 2010
Failure mitigation in optimal topology design using a coupled nonlinear continuum damage model James, Kai A.; Waisman, Haim Computer Methods in Applied Mechanics and Engineering, Vol. 268 https://doi.org/10.1016/j.cma.2013.10.022	journal	January 2014
A general framework for robust topology optimization under load-uncertainty including stress constraints Thore, Carl-Johan; Holmberg, Erik; Klarbring, Anders Computer Methods in Applied Mechanics and Engineering, Vol. 319 https://doi.org/10.1016/j.cma.2017.02.015	journal	June 2017
Stress-based topology optimization with discrete geometric components Zhang, Shanglong; Gain, Arun L.; Norato, Julián A. Computer Methods in Applied Mechanics and Engineering, Vol. 325 https://doi.org/10.1016/j.cma.2017.06.025	journal	October 2017
Stress-based shape and topology optimization with the level set method Picelli, R.; Townsend, S.; Brampton, C. Computer Methods in Applied Mechanics and Engineering, Vol. 329 https://doi.org/10.1016/j.cma.2017.09.001	journal	February 2018
A new multi-p-norm formulation approach for stress-based topology optimization design Kiyono, C. Y.; Vatanabe, S. L.; Silva, E. C. N. Composite Structures, Vol. 156 https://doi.org/10.1016/j.compstruct.2016.05.058	journal	November 2016
Minimum stress optimal design with the level set method Allaire, Grégoire; Jouve, François Engineering Analysis with Boundary Elements, Vol. 32, Issue 11 https://doi.org/10.1016/j.enganabound.2007.05.007	journal	November 2008
Topology optimization for simplified structural fire safety Madsen, Søren; Lange, Nis P.; Giuliani, Luisa Engineering Structures, Vol. 124 https://doi.org/10.1016/j.engstruct.2016.06.018	journal	October 2016
Topology optimization of continuum structures: A review* Eschenauer, Hans A.; Olhoff, Niels Applied Mechanics Reviews, Vol. 54, Issue 4 https://doi.org/10.1115/1.1388075	journal	July 2001
Block aggregation of stress constraints in topology optimization of structures París, J.; Navarrina, F.; Colominas, I. OPTI 2007, Computer Aided Optimum Design in Engineering X https://doi.org/10.2495/OP070031	conference	April 2007
New developments in handling stress constraints in optimal material distribution Duysinx, P.; Sigmund, O. 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization https://doi.org/10.2514/6.1998-4906	conference	February 2013

Cited By (4)

A numerical scheme for filter boundary conditions in topology optimization on regular and irregular meshes Kumar, Prabhat; Fernández, Eduardo arXiv https://doi.org/10.48550/arxiv.2101.01122	preprint	January 2021
An aggregation strategy of maximum size constraints in density-based topology optimization Fernández, Eduardo; Collet, Maxime; Alarcón, Pablo Structural and Multidisciplinary Optimization, Vol. 60, Issue 5 https://doi.org/10.1007/s00158-019-02313-8	journal	June 2019
Mixed projection- and density-based topology optimization with applications to structural assemblies Pollini, Nicolò; Amir, Oded Structural and Multidisciplinary Optimization, Vol. 61, Issue 2 https://doi.org/10.1007/s00158-019-02390-9	journal	September 2019
Minimum length scale constraints in multi-scale topology optimisation for additive manufacturing Liu, Jikai; Zheng, Yufan; Ahmad, Rafiq Virtual and Physical Prototyping, Vol. 14, Issue 3 https://doi.org/10.1080/17452759.2019.1584944	journal	March 2019

Similar Records

A dual mesh method with adaptivity for stress-constrained topology optimization

Journal Article · 2019 · Structural and Multidisciplinary Optimization · OSTI ID:1727272

White, Daniel A.; Choi, Youngsoo; Kudo, Jun

Stress‐constrained topology optimization of structures subjected to nonproportional loading

Journal Article · 2023 · International Journal for Numerical Methods in Engineering · OSTI ID:1959376

Granlund, Gunnar; Wallin, Mathias; Tortorelli, Daniel; +1 more

Adaptive mesh refinement in stress-constrained topology optimization

Journal Article · 2018 · Structural and Multidisciplinary Optimization · OSTI ID:1481053

Salazar de Troya, Miguel A.; Tortorelli, Daniel A.

Related Subjects

42 ENGINEERING
97 MATHEMATICS AND COMPUTING
Length scale
Stress constraints
Topology optimization

Title: Achieving stress-constrained topological design via length scale control

Citation Formats

References (48)

Cited By (4)

Similar Records

Related Subjects