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Structural and Multidisciplinary Optimization

, Volume 42, Issue 5, pp 725–738 | Cite as

Topology optimization involving thermo-elastic stress loads

  • Tong Gao
  • Weihong Zhang
Research Paper

Abstract

Structural topology optimization of thermo-elastic problems is investigated in this paper. The key issues about the penalty models of the element stiffness and thermal stress load of the finite element model are highlighted. The penalization of thermal stress coefficient (TSC) measured by the product between thermal expansion coefficient and Young’s modulus is proposed for the first time to characterize the dependence of the thermal stress load upon the design variables defined by element pseudo-densities. In such a way, the element stiffness and the thermal stress load can be penalized independently in terms of element pseudo-density. This formulation demonstrates especially its capability of solving problems with multiphase materials. Besides, the comparison study shows that the interpolation model RAMP is more advantageous than the SIMP in our case. Furthermore, sensitivity analysis of the structural mean compliance is developed in the case of steady-state heat conduction. Numerical examples of two-phase and three-phase materials are presented.

Keywords

Topology optimization Thermo-elastic problems Thermal stress Design-dependent load Thermal stress coefficient 

Notes

Acknowledgements

This work is supported by the National Science Fund for Distinguished Young Scholars (10925212), the National Natural Science Foundation of China (50775184, 90916027) and the Aeronautical Science Foundation (2008ZA53007).

References

  1. Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194:363–393MATHCrossRefMathSciNetGoogle Scholar
  2. Ansola R, Canales J, Tárrago AJ (2006) An efficient sensitivity computation strategy for the evolutionary structural optimization (ESO) of continuum structures subjected to self-weight loads. Finite Elem Anal Des 42:1220–1230CrossRefGoogle Scholar
  3. Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202CrossRefGoogle Scholar
  4. Bendsøe MP (1995) Optimization of structural topology, shape, and material. Springer, LondonGoogle Scholar
  5. Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654CrossRefGoogle Scholar
  6. Bruyneel M, Duysinx P (2005) Note on topology optimization of continuum structures including self-weight. Struct Multidisc Optim 29:245–256CrossRefGoogle Scholar
  7. Chen BC, Kikuchi N (2001) Topology optimisation with design dependent loads. Finite Elem Anal Des 39:57–70CrossRefGoogle Scholar
  8. Cho S, Choi JY (2005) Efficient topology optimization of thermo-elasticity problems using coupled field adjoint sensitivity analysis method. Finite Elem Anal Des 41:1481–1495CrossRefMathSciNetGoogle Scholar
  9. Du J, Olhoff N (2003a) Topological optimization of continuum structures with design-dependent surface loading—part I: new computational approach for 2D problems. Struct Multidisc Optim 27:166–177CrossRefMathSciNetGoogle Scholar
  10. Du J, Olhoff N (2003b) Topological optimization of continuum structures with design-dependent surface loading—part II: algorithm and examples for 3D problems. Struct Multidisc Optim 27:151–165CrossRefMathSciNetGoogle Scholar
  11. Fleury C, Braibant V (1986) Structural optimization: a new dual method using mixed variables. Int J Numer Methods Eng 23:409–428MATHCrossRefMathSciNetGoogle Scholar
  12. Fuchs MB, Moses E (2000) Optimal structural topologies with transmissible loads. Struct Multidisc Optim 19:263–273CrossRefGoogle Scholar
  13. Fuchs MB, Shemesh NNY (2004) Density-based topological design of structures subjected to water pressure using a parametric loading surface. Struct Multidisc Optim 28:11–19CrossRefGoogle Scholar
  14. Gao T, Zhang WH (2009a) Structural topology optimization under inertial loads. Chinese Journal of Theoretical Applied Mechanics 41(4):530–541 (in Chinese)Google Scholar
  15. Gao T, Zhang WH (2009b) Topology optimization of multiphase-material structures under design-dependent pressure loads. Int J Simul Multidisci Des Optim 3(1):297–306Google Scholar
  16. Gao T, Zhang WH, Zhu JH, Xu YJ, Bassir DH (2008) Topology optimization of heat conduction problem involving design dependent heat load effect. Finite Elem Anal Des 44:805–813CrossRefGoogle Scholar
  17. Hammer VB, Olhoff N (2000) Topology optimisation of continuum structures subjected to pressure loading. Struct Multidisc Optim 19:85–92CrossRefGoogle Scholar
  18. Li Q, Steven GP, Xie YM (1999) Displacement minimization of themoelastic structures by evolutionary thickness design. Comput Methods Appl Mech Eng 179:361–378MATHCrossRefGoogle Scholar
  19. Liu Z, Korvink JG, Huang R (2005) Structure topology optimization: fully coupled level set method via FEMLAB. Struct Multidisc Optim 29(6):407–417CrossRefMathSciNetGoogle Scholar
  20. Rodrigues H, Fernandes P (1995) A material based model for topology optimization of thermoelastic structures. Int J Numer Methods Eng 38:1951–1965MATHCrossRefMathSciNetGoogle Scholar
  21. Rozvany GIN (2010) A critical review of established methods of structural topology optimization. Struct Multidisc Optim 37:217–237CrossRefMathSciNetGoogle Scholar
  22. Rozvany GIN, Prager W (1979) A new class of structural optimisation problems: optimal arch grids. Comput Methods Appl Mech Eng 19:49–58CrossRefMathSciNetGoogle Scholar
  23. Rozvany GIN, Zhou M (1991) Applications of the COC algorithm in layout optimization. In: Eschenauer H, Matteck C, Olhoff N (eds) Engineering optimization in design processes. Proc. int. conf. held in Karlsruhe, Germany, Sept. 1990. Springer, Berlin, pp 59–70Google Scholar
  24. Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optim 4:250–254CrossRefGoogle Scholar
  25. Sigmund O, Clausen PM (2007) Topology optimization using a mixed formulation: an alternative way to solve pressure load problems. Comput Methods Appl Mech Eng 196:1874–1889MATHCrossRefMathSciNetGoogle Scholar
  26. Stolpe M, Svanberg K (2001) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidisc Optim 22:116–124CrossRefGoogle Scholar
  27. Sun SP, Zhang WH (2009) Topology optimal design of thermo-elastic structures. Chinese Journal of Theoretical Applied Mechanics 41(6):878–887 (in Chinese)Google Scholar
  28. Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24:359–373MATHCrossRefMathSciNetGoogle Scholar
  29. Svanberg K (1995) A globally convergent version of MMA without linesearch. In: Proc. first world congress of structural and multidisciplinary optimization. Pergamon, Oxford, pp 9–16Google Scholar
  30. Yang XY, Xie YM, Steven GP (2005) Evolutionary methods for topology optimization of continuous structures with design dependent loads. Comput Struct 83:956–963CrossRefGoogle Scholar
  31. Zhang WH, Fleury C (1997) A modification of convex approximation methods for structural optimization. Comput Struct 64:89–95MATHCrossRefMathSciNetGoogle Scholar
  32. Zhou M, Rozvany GIN (1991) The COC algorithm, part II: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89:309–336CrossRefGoogle Scholar
  33. Zuo KT, Qian Q, Zhao YD, Chen LP (2005) Research on the topology optimization about thermo-structural coupling field. Acta Mech Solida Sinica 26:447–452 (in Chinese)Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Engineering Simulation and Aerospace Computing (ESAC), The Key Laboratory of Contemporary Design and Integrated Manufacturing TechnologyNorthwestern Polytechnical UniversityXi’anChina

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