A level set method for topology optimization of continuum structures with bounded design domain

Article

Rong, Jian Hua and Liang, Qing Quan. 2008. "A level set method for topology optimization of continuum structures with bounded design domain." Computer Methods in Applied Mechanics and Engineering. 197 (17-18), pp. 1447-1465. https://doi.org/10.1016/j.cma.2007.11.026
Article Title

A level set method for topology optimization of continuum structures with bounded design domain

ERA Journal ID4173
Article CategoryArticle
AuthorsRong, Jian Hua (Author) and Liang, Qing Quan (Author)
Journal TitleComputer Methods in Applied Mechanics and Engineering
Journal Citation197 (17-18), pp. 1447-1465
Number of Pages19
Year2008
Place of PublicationNetherlands
ISSN0045-7825
Digital Object Identifier (DOI)https://doi.org/10.1016/j.cma.2007.11.026
Web Address (URL)http://www.sciencedirect.com/science/journal/00457825
Abstract

In practice, a continuum structure is usually designed to carry the traction applied to the boundary of the structure subject to prescribed displacements imposed on its boundary. The design domains of practical structures are often limited and significantly affect the final optimal design of the structures. Structural boundaries under traction and prescribed displacements should be treated as a zero level set in the level set methods. Firstly, to overcome the limitations of current level set methods and the stopping issue of structural boundary movements, this paper presents a set of new level set based optimization formulae for the optimal design of continuum structures with bounded design domains. A set of new normal velocities required by level set movements is given. A level set based optimization algorithm is developed and implemented with several robust and efficient numerical techniques, which include the level set regularization algorithm, gradient projection algorithm, nonlinear velocity mapping algorithm and return mapping algorithm. Secondly, in order to overcome the difficulty in nucleating holes in the design domain in the level set based optimization method, this paper introduces a new optimization strategy with a small possibility random topology mutations and crossovers. A mixed topology optimization algorithm is implemented and presented for the compliance minimization problems of continuum structures with material volume constraints. The validity and effectiveness of the proposed method are demonstrated with two examples.

Keywordsstructural optimization; topology optimization; level set method; random mutation
ANZSRC Field of Research 2020400510. Structural engineering
490407. Mathematical logic, set theory, lattices and universal algebra
490412. Topology
Public Notes

Files associated with this item cannot be displayed due to copyright restrictions.

Byline AffiliationsChangsha University of Science and Technology, China
University of New South Wales
Permalink -

https://research.usq.edu.au/item/9yq4y/a-level-set-method-for-topology-optimization-of-continuum-structures-with-bounded-design-domain

Log in to edit
  • 2231
    total views
  • 7
    total downloads
  • 2
    views this month
  • 0
    downloads this month

Export as

Related outputs

A topological optimization method considering stress constraints
Rong, Jian Hua, Liang, Qing Quan, Guo, Seng and Mu, Rang Ke. 2008. "A topological optimization method considering stress constraints ." Liu, Deshun, Wu, Yihu, Hou, Zhixiang and Wang, Junnian (ed.) ICICTA 2008: International Conference on Intelligent Computation Technology and Automation. Changsha, China 20 - 22 Oct 2008 Los Alamitos, CA. United States. https://doi.org/10.1109/ICICTA.2008.223
Structural design optimization
Liang, Qing Quan. 2007. "Structural design optimization." Advances in Structural Engineering: an international journal. 10 (6), pp. i-ii.
Preface [to the 2005 Australian Structural Engineering Conference (ASEC) issue of Australian Journal of Structural Engineering]
Uy, Brian and Liang, Qing Quan. 2007. "Preface [to the 2005 Australian Structural Engineering Conference (ASEC) issue of Australian Journal of Structural Engineering]." Australian Journal of Structural Engineering. 7 (2).
A performance index for topology and shape optimization of plate bending problems with displacement constraints
Liang, Qing Quan, Xie, Yi Min and Steven, Grant P.. 2001. "A performance index for topology and shape optimization of plate bending problems with displacement constraints ." Structural and Multidisciplinary Optimization. 21 (5), pp. 393-399. https://doi.org/10.1007/PL00013281
Ultimate strength of continuous composite beams in combined bending and shear
Liang, Qing Quan, Uy, Brian, Bradford, Mark A. and Ronagh, Hamid R.. 2004. "Ultimate strength of continuous composite beams in combined bending and shear ." Journal of Constructional Steel Research. 60 (8), pp. 1109-1128. https://doi.org/10.1016/j.jcsr.2003.12.001
Local buckling of steel plates in double skin composite panels under biaxial compression and shear
Liang, Qing Quan, Uy, Brian, Wright, Howard D. and Bradford, Mark A.. 2004. "Local buckling of steel plates in double skin composite panels under biaxial compression and shear ." Journal of Structural Engineering. 130 (3), pp. 443-451. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:3(443)
Generating optimal strut-and-tie models in prestressed concrete beams by performance-based optimization
Liang, Qing Quan, Xie, Yi Min and Steven, Grant P.. 2001. "Generating optimal strut-and-tie models in prestressed concrete beams by performance-based optimization ." ACI Structural Journal. 98 (2), pp. 226-232.
Strength analysis of steel-concrete composite beams in combined bending and shear
Liang, Qing Quan, Uy, Brian, Bradford, Mark A. and Ronagh, Hamid R.. 2005. "Strength analysis of steel-concrete composite beams in combined bending and shear ." Journal of Structural Engineering. 131 (10), pp. 1593-1600. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:10(1593)
Performance-based optimization for strut-tie modeling of structural concrete
Liang, Qing Quan, Uy, Brian and Steven, Grant P.. 2002. "Performance-based optimization for strut-tie modeling of structural concrete ." Journal of Structural Engineering. 128 (6), pp. 815-823. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:6(815)
A performance-based optimization method for topology design of continuum structures with mean compliance constraints
Liang, Qing Quan and Steven, Grant P.. 2002. "A performance-based optimization method for topology design of continuum structures with mean compliance constraints." Computer Methods in Applied Mechanics and Engineering. 191 (13-14), pp. 1471-1489.
Strength of concrete-filled steel box columns with buckling effects
Liang, Qing Quan, Uy, Brian and Liew, J. Y. Richard. 2007. "Strength of concrete-filled steel box columns with buckling effects." Australian Journal of Structural Engineering. 7 (2), pp. 145-155.
Closure to 'Strength analysis of steel-concrete composite beams in combined bending and shear' by Qing Quan Liang, Brian Uy, Mark A. Bradford and Hamid R. Ronagh
Liang, Qing Quan, Uy, Brian, Bradford, Mark A. and Ronagh, Hamid R.. 2007. "Closure to 'Strength analysis of steel-concrete composite beams in combined bending and shear' by Qing Quan Liang, Brian Uy, Mark A. Bradford and Hamid R. Ronagh." Journal of Structural Engineering. 133 (2), pp. 309-310. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:2(309)
Local buckling of steel plates in concrete-filled thin-walled steel tubular beam-columns
Liang, Qing Quan, Uy, Brian and Liew, J. Y. Richard. 2007. "Local buckling of steel plates in concrete-filled thin-walled steel tubular beam-columns." Journal of Constructional Steel Research. 63 (3), pp. 396-405. https://doi.org/10.1016/j.jcsr.2006.05.004
Post-local buckling of steel plates in concrete-filled thin-walled steel tubular columns under biaxial loading
Liang, Qing Quan. 2006. "Post-local buckling of steel plates in concrete-filled thin-walled steel tubular columns under biaxial loading." Kanok-Nukulchai, Worsak, Munasinghe, Sunil and Anwar, Naveed (ed.) 10th East Asia-Pacific Conference on Structural Engineering and Construction: Materials, Experimentation, Maintenance and Rehabilitation (EASEC-10). Bangkok, Thailand 03 - 05 Aug 2006 Thailand.
Performance-based optimization of strut-and-tie models in reinforced concrete beam-column connections
Liang, Qing Quan. 2006. "Performance-based optimization of strut-and-tie models in reinforced concrete beam-column connections." Kanok-Nukulchai, Worsak, Munasinghe, Sunil and Anwar, Naveed (ed.) 10th East Asia-Pacific Conference on Structural Engineering and Construction: Materials, Experimentation, Maintenance and Rehabilitation (EASEC-10). Bangkok, Thailand 03 - 05 Aug 2006 Thailand.
Performance-based analysis of concrete-filled steel tubular beam–columns, part I: theory and algorithms
Liang, Qing Quan. 2009. "Performance-based analysis of concrete-filled steel tubular beam–columns, part I: theory and algorithms." Journal of Constructional Steel Research. 65 (2), pp. 363-372. https://doi.org/10.1016/j.jcsr.2008.03.007
Performance-based analysis of concrete-filled steel tubular beam–columns, part II: verification and applications
Liang, Qing Quan. 2009. "Performance-based analysis of concrete-filled steel tubular beam–columns, part II: verification and applications." Journal of Constructional Steel Research. 65 (2), pp. 351-362. https://doi.org/10.1016/j.jcsr.2008.03.003
Geometric and material nonlinear behaviour of steel plates in thin-walled concrete filled box columns
Liang, Qing Quan and Uy, Brian. 1998. "Geometric and material nonlinear behaviour of steel plates in thin-walled concrete filled box columns." Shanmugam, N. E., Liew, J. Y. R. and Thevendran, V. (ed.) 2nd International Conference on Thin-Walled Structures. Singapore 02 - 04 Dec 1998 Oxford, UK.
Local and post-local buckling of steel-concrete composite panels under combined states of stresses
Liang, Qing Quan, Uy, Brian, Wright, Howard D. and Bradford, Mark A.. 2003. "Local and post-local buckling of steel-concrete composite panels under combined states of stresses." Hancock, G. J., Bradford, Mark A., Wilkinson, T. J., Uy, Brian and Rasmussen, K. J. R. (ed.) International Conference on Advances in Structures (ASSCCA'03). Sydney, Australia 22 - 25 Jun 2003 United Kingdom.
Strength of concrete-filled steel box columns with local buckling effects
Liang, Qing Quan, Uy, Brian and Liew, J. Y. Richard. 2005. "Strength of concrete-filled steel box columns with local buckling effects." Stewart, Mark G. and Dockrill, Brad (ed.) 2005 Australian Structural Engineering Conference (ASEC 2005). Newcastle, Australia 11 - 14 Sep 2005 Newcastle, Australia.
Nonlinear analysis of short concrete-filled steel tubular beam-columns under axial load and biaxial bending
Liang, Qing Quan. 2008. "Nonlinear analysis of short concrete-filled steel tubular beam-columns under axial load and biaxial bending." Journal of Constructional Steel Research. 64 (3), pp. 295-304. https://doi.org/10.1016/j.jcsr.2007.07.001
Performance-based optimization: a review
Liang, Qing Quan. 2007. "Performance-based optimization: a review." Advances in Structural Engineering: an international journal. 10 (6), pp. 739-753.
A level set method with maximum design domain limits
Rong, J. H., Yi, J. H. and Liang, Q. Q.. 2008. "A level set method with maximum design domain limits." Xie, Yi Min and Patnaikuni, Indubhushan (ed.) ISEC 4: Innovations in Structural Engineering and Construction. Melbourne, Australia 26 - 28 Sep 2007 London, United Kingdom.
Nonlinear analysis and behavior of concrete-filled steel tubular beam-columns
Liang, Q. Q. and Hadi, M. N. S.. 2008. "Nonlinear analysis and behavior of concrete-filled steel tubular beam-columns." Xie, Yi Min and Patnaikuni, Indubhushan (ed.) ISEC 4: Innovations in Structural Engineering and Construction. Melbourne, Australia 26 - 28 Sep 2007 London, United Kingdom.
Performance-based optimization of strut-and-tie models in reinforced concrete deep beams
Liang, Q. Q. and Ng, A. W. M.. 2008. "Performance-based optimization of strut-and-tie models in reinforced concrete deep beams." Xie, Yi Min and Patnaikuni, Indubhushan (ed.) ISEC 4: Innovations in Structural Engineering and Construction. Melbourne, Australia 26 - 28 Sep 2007 Netherlands.
Effects of continuum design domains on optimal bracing systems for multistory steel building frameworks
Liang, Qing Quan. 2007. "Effects of continuum design domains on optimal bracing systems for multistory steel building frameworks." Veidt, Martin, Albermani, Faris, Daniel, Bill, Griffiths, John, Hargreaves, Doug, McAree, Ross, Meehan, Paul and Tan, Andy (ed.) 5th Australasian Congress on Applied Mechanics (ACAM 2007). Brisbane, Australia 10 - 12 Dec 2007 Sydney, Australia.
Automated performance-based optimal design of continuum structures under multiple load cases
Liang, Qing Quan. 2007. "Automated performance-based optimal design of continuum structures under multiple load cases." Veidt, Martin, Albermani, Faris, Daniel, Bill, Griffiths, John, Hargreaves, Doug, McAree, Ross, Meehan, Paul and Tan, Andy (ed.) 5th Australasian Congress on Applied Mechanics (ACAM 2007). Brisbane, Australia 10 - 12 Dec 2007 Sydney, Australia.
Optimal topology selection of continuum structures with stress and displacement constraints
Liang, Qing Quan, Xie, Yi Min and Steven, Grant P.. 1999. "Optimal topology selection of continuum structures with stress and displacement constraints." Okamura, Hajime and Shima, Hiroshi (ed.) 7th East Asia-Pacific Conference on Structural Engineering & Construction. Kochi, Japan 27 - 29 Aug 1999 Tokyo, Japan.
Topology optimization of strut-and-tie models in non-flexural reinforced concrete members
Liang, Qing Quan, Xie, Yi Min, Steven, Grant P. and Schmidt, L. C.. 1999. "Topology optimization of strut-and-tie models in non-flexural reinforced concrete members." Hadi, Muhammad N. S. and Schmidt, L. C. (ed.) International Conference on Mechanics of Structures, Materials and Systems (1999). Wollongong, Australia 17 - 19 Feb 1999 Wollongong, Australia.
Local buckling of biaxially compressed steel plates in double skin composite panels
Liang, Qing Quan, Uy, Brian, Wright, Howard D. and Bradford, Mark A.. 2002. "Local buckling of biaxially compressed steel plates in double skin composite panels." Chan, S. L., Teng, J. G. and Chung, K. F. (ed.) Third International Conference on Advances in Steel Structures (2002). Hong Kong, China 09 - 11 Dec 2002 London, UK.
Local and post-local buckling of double skin composite panels
Liang, Qing Quan, Uy, Brian, Wright, Howard D. and Bradford, Mark A.. 2003. "Local and post-local buckling of double skin composite panels ." Proceedings of the Institution of Civil Engineers: Structures and Buildings. 156 (2), pp. 111-119.
Performance-based optimization of structures: theory and applications
Liang, Qing Quan. 2005. Performance-based optimization of structures: theory and applications. London and New York. Spon Press.
Nonlinear analysis of concrete-filled thin-walled steel box columns with local buckling effects
Liang, Qing Quan, Uy, Brian and Liew, J. Y. Richard. 2006. "Nonlinear analysis of concrete-filled thin-walled steel box columns with local buckling effects." Journal of Constructional Steel Research. 62 (6), pp. 581-591. https://doi.org/10.1016/j.jcsr.2005.09.007
Inelastic behavior of concrete-filled thin-walled steel tubular columns subjected to local buckling
Liang, Qing Quan. 2006. "Inelastic behavior of concrete-filled thin-walled steel tubular columns subjected to local buckling." Kanok-Nukulchai, Worsak, Munasinghe, Sunil and Anwar, Naveed (ed.) 10th East Asia-Pacific Conference on Structural Engineering and Construction: Materials, Experimentation, Maintenance and Rehabilitation (EASEC-10). Bangkok, Thailand 03 - 05 Aug 2006 Pathumthani, Thailand.