Topology optimization of compliant mechanisms under transient thermal conditions

Granlund, Gunnar; Wallin, Mathias; Günther-Hanssen, Olov; Tortorelli, Daniel; Watts, Seth

doi:10.1016/j.cma.2023.116478

Title: Topology optimization of compliant mechanisms under transient thermal conditions

Abstract

This work considers multi-material topology optimization of compliant mechanisms under transient thermal and quasi-static mechanical conditions wherein thermally actuated devices are optimized for different operating conditions. The materials are modeled using finite strain thermo-hyperelasticity and a two way coupling between the energy balance and equilibrium equations is investigated. The design updates are generated from the gradient-based method of moving asymptotes optimizer and the sensitivities are computed using the time dependent adjoint sensitivity analysis. Results show the impact of designing for short versus long actuation times.

Authors:

^[1];

^[1]; Tortorelli, Daniel ^[2];

^[3]

Lund Univ. (Sweden)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States). Center for Design and Optimization; Univ. of Illinois at Urbana-Champaign, IL (United States)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States). Center for Design and Optimization

Publication Date:: Tue Oct 03 00:00:00 EDT 2023

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

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 2248144

Report Number(s):: LLNL-JRNL-849277
Journal ID: ISSN 0045-7825; 1074842

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: Computer Methods in Applied Mechanics and Engineering

Additional Journal Information:: Journal Volume: 418; Journal Issue: A; Journal ID: ISSN 0045-7825

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; Topology optimization; Finite strain thermo-hyperelasticity; Transients; Multi-material; Compliant mechanisms; Thermally actuated devices

Citation Formats


                    Granlund, Gunnar, Wallin, Mathias, Günther-Hanssen, Olov, Tortorelli, Daniel, and Watts, Seth. Topology optimization of compliant mechanisms under transient thermal conditions.  United States: N. p., 2023. 
Web.  doi:10.1016/j.cma.2023.116478.

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                    Granlund, Gunnar, Wallin, Mathias, Günther-Hanssen, Olov, Tortorelli, Daniel, & Watts, Seth. Topology optimization of compliant mechanisms under transient thermal conditions.  United States.  https://doi.org/10.1016/j.cma.2023.116478

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                    Granlund, Gunnar, Wallin, Mathias, Günther-Hanssen, Olov, Tortorelli, Daniel, and Watts, Seth. Tue .  
"Topology optimization of compliant mechanisms under transient thermal conditions".  United States.  https://doi.org/10.1016/j.cma.2023.116478.  https://www.osti.gov/servlets/purl/2248144.

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@article{osti_2248144,

  title        = {Topology optimization of compliant mechanisms under transient thermal conditions},

  author       = {Granlund, Gunnar and Wallin, Mathias and Günther-Hanssen, Olov and Tortorelli, Daniel and Watts, Seth},

  abstractNote = {This work considers multi-material topology optimization of compliant mechanisms under transient thermal and quasi-static mechanical conditions wherein thermally actuated devices are optimized for different operating conditions. The materials are modeled using finite strain thermo-hyperelasticity and a two way coupling between the energy balance and equilibrium equations is investigated. The design updates are generated from the gradient-based method of moving asymptotes optimizer and the sensitivities are computed using the time dependent adjoint sensitivity analysis. Results show the impact of designing for short versus long actuation times.},

  doi          = {10.1016/j.cma.2023.116478},

  journal      = {Computer Methods in Applied Mechanics and Engineering},

  number       = A,

  volume       = 418,

  place        = {United States},

  year         = {Tue Oct 03 00:00:00 EDT 2023},

  month        = {Tue Oct 03 00:00:00 EDT 2023}

}

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Works referenced in this record:

Achieving minimum length scale in topology optimization using nodal design variables and projection functions
journal, August 2004

Guest, J. K.; Prévost, J. H.; Belytschko, T.
International Journal for Numerical Methods in Engineering, Vol. 61, Issue 2
DOI: 10.1002/nme.1064

Topology optimization of heat conduction problems using the finite volume method
journal, March 2006

Gersborg-Hansen, A.; Bendsøe, M. P.; Sigmund, O.
Structural and Multidisciplinary Optimization, Vol. 31, Issue 4
DOI: 10.1007/s00158-005-0584-3

?-relaxed approach in structural topology optimization
journal, June 1997

Cheng, G. D.; Guo, X.
Structural Optimization, Vol. 13, Issue 4
DOI: 10.1007/BF01197454

Topology optimization approaches: A comparative review
journal, August 2013

Sigmund, Ole; Maute, Kurt
Structural and Multidisciplinary Optimization, Vol. 48, Issue 6
DOI: 10.1007/s00158-013-0978-6

Topology optimization of compliant mechanisms considering strain variance
journal, June 2020

Niu, Bin; Liu, Xiaolong; Wallin, Mathias
Structural and Multidisciplinary Optimization, Vol. 62, Issue 3
DOI: 10.1007/s00158-020-02632-1

Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems
journal, July 2014

Wang, Fengwen; Lazarov, Boyan Stefanov; Sigmund, Ole
Computer Methods in Applied Mechanics and Engineering, Vol. 276
DOI: 10.1016/j.cma.2014.03.021

Design of materials with extreme thermal expansion using a three-phase topology optimization method
journal, June 1997

Sigmund, O.; Torquato, S.
Journal of the Mechanics and Physics of Solids, Vol. 45, Issue 6
DOI: 10.1016/S0022-5096(96)00114-7

Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity
journal, July 1994

Michaleris, Panagiotis; Tortorelli, Daniel A.; Vidal, Creto A.
International Journal for Numerical Methods in Engineering, Vol. 37, Issue 14
DOI: 10.1002/nme.1620371408

Material interpolation schemes for unified topology and multi-material optimization
journal, January 2011

Hvejsel, Christian Frier; Lund, Erik
Structural and Multidisciplinary Optimization, Vol. 43, Issue 6
DOI: 10.1007/s00158-011-0625-z

Adaptive mesh refinement in stress-constrained topology optimization
journal, October 2018

Salazar de Troya, Miguel A.; Tortorelli, Daniel A.
Structural and Multidisciplinary Optimization, Vol. 58, Issue 6
DOI: 10.1007/s00158-018-2084-2

Comparison of isotropic hardening and kinematic hardening in thermoplasticity
journal, July 2005

Hakansson, P.; Wallin, M.; Ristinmaa, M.
International Journal of Plasticity, Vol. 21, Issue 7
DOI: 10.1016/j.ijplas.2004.07.002

On projection methods, convergence and robust formulations in topology optimization
journal, December 2010

Wang, Fengwen; Lazarov, Boyan Stefanov; Sigmund, Ole
Structural and Multidisciplinary Optimization, Vol. 43, Issue 6
DOI: 10.1007/s00158-010-0602-y

Stress-constrained topology optimization for compliant mechanism design
journal, July 2015

De Leon, Daniel M.; Alexandersen, Joe; O. Fonseca, Jun S.
Structural and Multidisciplinary Optimization, Vol. 52, Issue 5
DOI: 10.1007/s00158-015-1279-z

A unified aggregation and relaxation approach for stress-constrained topology optimization
journal, July 2016

Verbart, Alexander; Langelaar, Matthijs; Keulen, Fred van
Structural and Multidisciplinary Optimization, Vol. 55, Issue 2
DOI: 10.1007/s00158-016-1524-0

Filters in topology optimization based on Helmholtz-type differential equations
journal, December 2010

Lazarov, B. S.; Sigmund, O.
International Journal for Numerical Methods in Engineering, Vol. 86, Issue 6
DOI: 10.1002/nme.3072

Topology optimization of continuum structures with local stress constraints
journal, December 1998

Duysinx, P.; Bendsøe, M. P.
International Journal for Numerical Methods in Engineering, Vol. 43, Issue 8
DOI: 10.1002/(SICI)1097-0207(19981230)43:8<1453::AID-NME480>3.0.CO;2-2

Eigenfrequency constrained topology optimization of finite strain hyperelastic structures
journal, May 2020

Dalklint, Anna; Wallin, Mathias; Tortorelli, Daniel A.
Structural and Multidisciplinary Optimization, Vol. 61, Issue 6
DOI: 10.1007/s00158-020-02557-9

Consistent boundary conditions for PDE filter regularization in topology optimization
journal, April 2020

Wallin, Mathias; Ivarsson, Niklas; Amir, Oded
Structural and Multidisciplinary Optimization, Vol. 62, Issue 3
DOI: 10.1007/s00158-020-02556-w

Level-set topology optimization considering nonlinear thermoelasticity
journal, April 2020

Chung, Hayoung; Amir, Oded; Kim, H. Alicia
Computer Methods in Applied Mechanics and Engineering, Vol. 361
DOI: 10.1016/j.cma.2019.112735

Topology optimization involving thermo-elastic stress loads
journal, June 2010

Gao, Tong; Zhang, Weihong
Structural and Multidisciplinary Optimization, Vol. 42, Issue 5
DOI: 10.1007/s00158-010-0527-5

Topology optimization of thermally actuated compliant mechanisms considering time-transient effect
journal, July 2004

Li, Ying; Saitou, Kazuhiro; Kikuchi, Noboru
Finite Elements in Analysis and Design, Vol. 40, Issue 11
DOI: 10.1016/j.finel.2003.05.002

Topology optimization for minimizing the maximum temperature of transient heat conduction structure
journal, January 2019

Wu, Shuhao; Zhang, Yongcun; Liu, Shutian
Structural and Multidisciplinary Optimization, Vol. 60, Issue 1
DOI: 10.1007/s00158-019-02196-9

Topology optimization for linear thermo-mechanical transient problems: Modal reduction and adjoint sensitivities: Topology Optimization for Transient Thermo-Mechanical Problems
journal, October 2017

Hooijkamp, E. C.; Keulen, F. van
International Journal for Numerical Methods in Engineering, Vol. 113, Issue 8
DOI: 10.1002/nme.5635

Topology optimization of thermo-elastic structures with multiple materials under mass constraint
journal, September 2016

Gao, Tong; Xu, Pengli; Zhang, Weihong
Computers & Structures, Vol. 173
DOI: 10.1016/j.compstruc.2016.06.002

A material based model for topology optimization of thermoelastic structures
journal, June 1995

Rodrigues, H.; Fernandes, P.
International Journal for Numerical Methods in Engineering, Vol. 38, Issue 12
DOI: 10.1002/nme.1620381202

An alternative interpolation scheme for minimum compliance topology optimization
journal, September 2001

Stolpe, M.; Svanberg, K.
Structural and Multidisciplinary Optimization, Vol. 22, Issue 2
DOI: 10.1007/s001580100129

Topology optimization of heat conduction problem involving design-dependent heat load effect
journal, October 2008

Gao, T.; Zhang, W. H.; Zhu, J. H.
Finite Elements in Analysis and Design, Vol. 44, Issue 14
DOI: 10.1016/j.finel.2008.06.001

Stress-based topology optimization for continua
journal, October 2009

Le, Chau; Norato, Julian; Bruns, Tyler
Structural and Multidisciplinary Optimization, Vol. 41, Issue 4
DOI: 10.1007/s00158-009-0440-y

A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations
journal, January 2002

Svanberg, Krister
SIAM Journal on Optimization, Vol. 12, Issue 2
DOI: 10.1137/S1052623499362822

Topology Optimization of the Transient Heat Conduction Problem on a Triangular Mesh
journal, May 2013

Zhuang, Chungang; Xiong, Zhenhua; Ding, Han
Numerical Heat Transfer, Part B: Fundamentals, Vol. 64, Issue 3
DOI: 10.1080/10407790.2013.791785

Experimental study on the seismic performance of a double-span traditional timber frame
journal, September 2015

Li, Xiaowei; Zhao, Junhai; Ma, Guowei
Engineering Structures, Vol. 98
DOI: 10.1016/j.engstruct.2015.04.031

Maximization of eigenvalues using topology optimization
journal, August 2000

Pedersen, N. L.
Structural and Multidisciplinary Optimization, Vol. 20, Issue 1
DOI: 10.1007/s001580050130

A review about the engineering design of optimal heat transfer systems using topology optimization
journal, February 2017

Dbouk, T.
Applied Thermal Engineering, Vol. 112
DOI: 10.1016/j.applthermaleng.2016.10.134

Design of multiphysics actuators using topology optimization – Part II: Two-material structures
journal, October 2001

Sigmund, O.
Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 49-50
DOI: 10.1016/S0045-7825(01)00252-3

Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation
journal, July 1992

Simo, J. C.; Miehe, C.
Computer Methods in Applied Mechanics and Engineering, Vol. 98, Issue 1
DOI: 10.1016/0045-7825(92)90170-O

Manufacturing tolerant topology optimization
journal, March 2009

Sigmund, Ole
Acta Mechanica Sinica, Vol. 25, Issue 2
DOI: 10.1007/s10409-009-0240-z

Topology optimization with manufacturing constraints: A unified projection-based approach
journal, October 2016

Vatanabe, Sandro L.; Lippi, Tiago N.; Lima, Cícero R. de
Advances in Engineering Software, Vol. 100
DOI: 10.1016/j.advengsoft.2016.07.002

Design of multiphysics actuators using topology optimization – Part I: One-material structures
journal, October 2001

Sigmund, O.
Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 49-50
DOI: 10.1016/S0045-7825(01)00251-1

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Title: Topology optimization of compliant mechanisms under transient thermal conditions

Abstract

Citation Formats

Achieving minimum length scale in topology optimization using nodal design variables and projection functions journal, August 2004

Topology optimization of heat conduction problems using the finite volume method journal, March 2006

?-relaxed approach in structural topology optimization journal, June 1997

Topology optimization approaches: A comparative review journal, August 2013

Topology optimization of compliant mechanisms considering strain variance journal, June 2020

Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems journal, July 2014

Design of materials with extreme thermal expansion using a three-phase topology optimization method journal, June 1997

Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity journal, July 1994

Material interpolation schemes for unified topology and multi-material optimization journal, January 2011

Adaptive mesh refinement in stress-constrained topology optimization journal, October 2018

Comparison of isotropic hardening and kinematic hardening in thermoplasticity journal, July 2005

On projection methods, convergence and robust formulations in topology optimization journal, December 2010

Stress-constrained topology optimization for compliant mechanism design journal, July 2015

A unified aggregation and relaxation approach for stress-constrained topology optimization journal, July 2016

Filters in topology optimization based on Helmholtz-type differential equations journal, December 2010

Topology optimization of continuum structures with local stress constraints journal, December 1998

Eigenfrequency constrained topology optimization of finite strain hyperelastic structures journal, May 2020

Consistent boundary conditions for PDE filter regularization in topology optimization journal, April 2020

Level-set topology optimization considering nonlinear thermoelasticity journal, April 2020

Topology optimization involving thermo-elastic stress loads journal, June 2010

Topology optimization of thermally actuated compliant mechanisms considering time-transient effect journal, July 2004

Topology optimization for minimizing the maximum temperature of transient heat conduction structure journal, January 2019

Topology optimization for linear thermo-mechanical transient problems: Modal reduction and adjoint sensitivities: Topology Optimization for Transient Thermo-Mechanical Problems journal, October 2017

Topology optimization of thermo-elastic structures with multiple materials under mass constraint journal, September 2016

A material based model for topology optimization of thermoelastic structures journal, June 1995

An alternative interpolation scheme for minimum compliance topology optimization journal, September 2001

Topology optimization of heat conduction problem involving design-dependent heat load effect journal, October 2008

Stress-based topology optimization for continua journal, October 2009

A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations journal, January 2002

Topology Optimization of the Transient Heat Conduction Problem on a Triangular Mesh journal, May 2013

Experimental study on the seismic performance of a double-span traditional timber frame journal, September 2015

Maximization of eigenvalues using topology optimization journal, August 2000

A review about the engineering design of optimal heat transfer systems using topology optimization journal, February 2017

Design of multiphysics actuators using topology optimization – Part II: Two-material structures journal, October 2001

Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation journal, July 1992

Manufacturing tolerant topology optimization journal, March 2009

Topology optimization with manufacturing constraints: A unified projection-based approach journal, October 2016

Design of multiphysics actuators using topology optimization – Part I: One-material structures journal, October 2001

Achieving minimum length scale in topology optimization using nodal design variables and projection functions
journal, August 2004

Topology optimization of heat conduction problems using the finite volume method
journal, March 2006

?-relaxed approach in structural topology optimization
journal, June 1997

Topology optimization approaches: A comparative review
journal, August 2013

Topology optimization of compliant mechanisms considering strain variance
journal, June 2020

Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems
journal, July 2014

Design of materials with extreme thermal expansion using a three-phase topology optimization method
journal, June 1997

Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity
journal, July 1994

Material interpolation schemes for unified topology and multi-material optimization
journal, January 2011

Adaptive mesh refinement in stress-constrained topology optimization
journal, October 2018

Comparison of isotropic hardening and kinematic hardening in thermoplasticity
journal, July 2005

On projection methods, convergence and robust formulations in topology optimization
journal, December 2010

Stress-constrained topology optimization for compliant mechanism design
journal, July 2015

A unified aggregation and relaxation approach for stress-constrained topology optimization
journal, July 2016

Filters in topology optimization based on Helmholtz-type differential equations
journal, December 2010

Topology optimization of continuum structures with local stress constraints
journal, December 1998

Eigenfrequency constrained topology optimization of finite strain hyperelastic structures
journal, May 2020

Consistent boundary conditions for PDE filter regularization in topology optimization
journal, April 2020

Level-set topology optimization considering nonlinear thermoelasticity
journal, April 2020

Topology optimization involving thermo-elastic stress loads
journal, June 2010

Topology optimization of thermally actuated compliant mechanisms considering time-transient effect
journal, July 2004

Topology optimization for minimizing the maximum temperature of transient heat conduction structure
journal, January 2019

Topology optimization for linear thermo-mechanical transient problems: Modal reduction and adjoint sensitivities: Topology Optimization for Transient Thermo-Mechanical Problems
journal, October 2017

Topology optimization of thermo-elastic structures with multiple materials under mass constraint
journal, September 2016

A material based model for topology optimization of thermoelastic structures
journal, June 1995

An alternative interpolation scheme for minimum compliance topology optimization
journal, September 2001

Topology optimization of heat conduction problem involving design-dependent heat load effect
journal, October 2008

Stress-based topology optimization for continua
journal, October 2009

A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations
journal, January 2002

Topology Optimization of the Transient Heat Conduction Problem on a Triangular Mesh
journal, May 2013

Experimental study on the seismic performance of a double-span traditional timber frame
journal, September 2015

Maximization of eigenvalues using topology optimization
journal, August 2000

A review about the engineering design of optimal heat transfer systems using topology optimization
journal, February 2017

Design of multiphysics actuators using topology optimization – Part II: Two-material structures
journal, October 2001

Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation
journal, July 1992

Manufacturing tolerant topology optimization
journal, March 2009

Topology optimization with manufacturing constraints: A unified projection-based approach
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Design of multiphysics actuators using topology optimization – Part I: One-material structures
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