Structural and Multidisciplinary Optimization

, Volume 56, Issue 4, pp 865–884 | Cite as

A novel displacement constrained optimization approach for black and white structural topology designs under multiple load cases

  • Jian Hua Rong
  • Liaohong Yu
  • Xuan Pei Rong
  • Zhi Jun Zhao
RESEARCH PAPER
  • 743 Downloads

Abstract

The gray problem of displacement constrained topology volume minimization under multiple load cases still is an opening topic of research. A series of topologies with clear profiles generated from an optimization process are very beneficial to method engineering applications. In this paper, a novel displacement constrained optimization approach for black and white structural topology designs under multiple load cases, is proposed to obtain a series of topologies with clear profiles. Firstly, a distribution feature of constraint displacement derivatives is investigated. Secondly, an adaptive adjusting approach of design variable bounds is proposed, and an improved approximate model with varied constraint limits and a volume penalty objective function are constructed. Thirdly, an improved density-based optimization method is proposed for the displacement constrained topology volume minimization under multiple load cases. Finally, several examples are given to demonstrate that the results obtained by the proposed method provide a series of topologies with clear profiles during an optimization process. It is concluded from examples that the proposed method is effective and robust for generating an optimal topology.

Keywords

Structural topology optimization Feasible domain adjustment Trust region Multiple constraints Dual algorithm 

References

  1. Bruns TE (2005) A reevaluation of the SIMP method with filtering and an alternative formulation for solid-void topology optimization. Struct. Multidisc. Optim. 30:428–436CrossRefGoogle Scholar
  2. Burden R, Faires J (1985) Numerical analysis, 3rd edn. Prindle, Weber and Schmidt, BostonMATHGoogle Scholar
  3. Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct. Multidisc. Optim. 49:1–38MathSciNetCrossRefGoogle Scholar
  4. Deng S, Suresh K (2015) Multi-constrained topology optimization via the topological sensitivity. Struct. Multidisc. Optim. 51:987–1001MathSciNetCrossRefGoogle Scholar
  5. Du J, Taylor JE (2002) Application of an energy-based model for the optimal design of structural materials and topology. Struct. Multidisc. Optim. 24:277–292CrossRefGoogle Scholar
  6. Fleury C (1989) Efficient approximation concepts using second order information. Int. J. Numer. Meth. Eng. 28:2041–2058MathSciNetCrossRefMATHGoogle Scholar
  7. Fuchs MB, Jiny S, Peleg N (2005) The SRV constraint for 0/1 topological design. Struct. Multidisc. Optim. 30:320–326CrossRefGoogle Scholar
  8. Fujii D, Kikuchi N (2000) Improvement of numerical instabilities in topology optimization using the SLP method. Struct Multidisc Optim 19:113–121CrossRefGoogle Scholar
  9. Garcia-Lopez NP, Sanchez-Silva M, Medaglia AL, Chateauneuf A (2011) A hybrid topology optimization methodology combining simulated annealing and SIMP. Comput Struct 89:1512–1522CrossRefGoogle Scholar
  10. Groenwold AA, Etman LFP (2009) A simple heuristic for gray-scale suppression in optimality criterion-based topology optimization. Struct. Multidisc. Optim. 39:217–225CrossRefGoogle Scholar
  11. Groenwold AA, Wood DW, Etman LFP, Tosserams S (2009) Globally convergent optimization algorithm using conservative convex separable diagonal quadratic approximations. AIAA J 47:2649–2657CrossRefGoogle Scholar
  12. Guedes JM, Taylor JE (1997) On the prediction of material properties and topology for optimal continuum structures. Struct. Optim. 14:193–199CrossRefGoogle Scholar
  13. Guest JK, Prevost JH, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int. J. Numer. Meth. Eng. 61(2):238–254MathSciNetCrossRefMATHGoogle Scholar
  14. Haber RB (1996) A new approach to variable-topology shape design using a constraint on perimeter. Struct. Optim. 11:1–12MathSciNetCrossRefGoogle Scholar
  15. Huang X, Xie YM (2007) Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem Anal Des 43(14):1039–1049CrossRefGoogle Scholar
  16. Huang X, Xie YM (2010) Evolutionary topology optimization of continuum structures with an additional displacement constraint. Struct Multidiscip Optim 40:409–416MathSciNetCrossRefMATHGoogle Scholar
  17. Jang GW, Kim MJ, Kim YY (2009) Design optimization of compliant mechanisms consisting of standardized elements. ASME Journal of Mechanical Design 131:121006CrossRefGoogle Scholar
  18. Kikuchi N, Nishiwaki S, Fonseca JSO, Silva ECN (1998) Design optimization method for compliant mechanisms and material microstructure. Comput Methods Appl Mech Eng 151:401–417MathSciNetCrossRefMATHGoogle Scholar
  19. Liang QQ, Xie YM, Steven GP (2001) A performance index for topology and shape optimization of plate bending problems with displacement constraints. Struct Multidiscip Optim 21:393–399CrossRefGoogle Scholar
  20. Liu XJ, Li ZD, Chen X (2011) A new solution for topology optimization problems with multiple loads: the guide-weight method. Sci China Tech Sci 54:1505–1514CrossRefMATHGoogle Scholar
  21. Nocedal J, Wright SJ (1999) Numerical Optimization. Springer, New YorkCrossRefMATHGoogle Scholar
  22. Olhoff N, Bendsøe MP, Rasmussen J (1991) On CAD-integrated structural topology and design optimization. Comput Methods Appl Mech Eng 89:259–279CrossRefMATHGoogle Scholar
  23. Petersson J, Sigmund O (1998) Slope constrained topology optimization. Int. J. Numer. Meth. Eng. 41:1417–1434MathSciNetCrossRefMATHGoogle Scholar
  24. Rietz A (2001) Sufficiency of a finite exponent in SIMP (power law) methods. Struct Multidiscip Optim 21:159–163CrossRefGoogle Scholar
  25. Rong JH, Yi JH (2010) A structural topological optimization method for multi-displacement constraint problems and any initial topology configuration. International Journal of Acta Mechanica Sinica 26:735–744CrossRefMATHGoogle Scholar
  26. Rong JH, Liu XH, Yi JJ (2011) An efficient structural topological optimization method for continuum structures with multiple displacement constraints. International Journal of Finite Elements in Analysis and Design 47:913–921CrossRefGoogle Scholar
  27. Rong JH, Xiao TT, Yu LH et al (2016) Continuum structural topological optimization with stress constraints based on an active constraint technique. Int J Numer Meth Eng 108(4):326–360MathSciNetCrossRefGoogle Scholar
  28. Sauter M, Kress G, Giger M, Ermanni P (2008) Complex shaped beam element and graph-based optimization of compliant mechanisms. Struct. Multidisc. Optim. 36:429–442MathSciNetCrossRefMATHGoogle Scholar
  29. Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct. Multidisc. Optim. 21(2):120–127MathSciNetCrossRefGoogle Scholar
  30. Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidisc Opt 33:401–424CrossRefGoogle Scholar
  31. Sigmund O, Maute K (2013) Topology optimization approaches: a comparative review. Struct. Multidisc. Opt. 48(6):1031–1055CrossRefGoogle Scholar
  32. Sigmund O, Peterson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards. Mesh dependencies and local minima. Struct. Optim. 16:68–75CrossRefGoogle Scholar
  33. Sobieski SJ, Haftka RT (1997) Multidisciplinary aerospace design optimization: survey of recent developments. Struct Optim 14:1–23CrossRefGoogle Scholar
  34. Stolpe M, Svanberg K (2001a) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidisc Optim 22:116–124CrossRefGoogle Scholar
  35. Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24:359–373MathSciNetCrossRefMATHGoogle Scholar
  36. Tang MY (2014) Trust region algorithm with two sub-problems for bound constrained problems. Applied Math and Comput 242:778–789MathSciNetMATHGoogle Scholar
  37. Wang MY, Wang S (2005) Bilateral filtering for structural topology optimization. Int J Numer Methods Eng 63:1911–1938MathSciNetCrossRefMATHGoogle Scholar
  38. Werme M (2008) Using the sequential linear integer programming method as a post-processor for stress-constrained topology optimization problems. Int J Numer Methods Eng 76:1544–1567MathSciNetCrossRefMATHGoogle Scholar
  39. Wood DW, Groenwold AA (2010) On concave constraint functions and duality in predominantly black-and-white topology optimization. Comput Methods Appl Mech Eng 199:2224–2234MathSciNetCrossRefMATHGoogle Scholar
  40. Xia L, Zhu JH, Zhang WH (2012) Sensitivity analysis with the modified Heaviside function for the optimal layout design of multi-component systems. Comput Methods Appl Mech Engrg 241–244:142–154MathSciNetCrossRefMATHGoogle Scholar
  41. Yin L, Yang W (2001) Optimality criteria method for topology optimization under multiple constraints. Comput Struct 79:1839–1850CrossRefGoogle Scholar
  42. Zhou M, Rozvany GIN (1991) The COC algorithm, part II: topological, geometry and generalized shape optimization. Comput Methods Appl Mech Eng 89:197–224CrossRefGoogle Scholar
  43. Zuo ZH, Xie YM (2014) Evolutionary topology optimization of continuum structures with a global displacement control. Comput Aided Des 56:58–67CrossRefGoogle Scholar
  44. Zuo ZH, Xie YM, Huang X (2012) Evolutionary topology optimization of structures with multiple displacement and frequency constraints. Adv Struct Eng 15(2):385–398CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Jian Hua Rong
    • 1
    • 2
  • Liaohong Yu
    • 1
    • 3
  • Xuan Pei Rong
    • 1
    • 2
  • Zhi Jun Zhao
    • 2
    • 4
  1. 1.School of Automotive and Mechanical EngineeringChangsha University of Science and TechnologyChangshaPeople’s Republic of China
  2. 2.Key Laboratory of Lightweight and Reliability Technology for Engineering VehicleCollege of Hunan ProvinceChangshaChina
  3. 3.School of Physical Science and TechnologyYichun UniversityYichunPeople’s Republic of China
  4. 4.Department of Civil EngineeringChangsha UniversityChangshaPeople’s Republic of China

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