Advertisement

Structural optimization

, Volume 12, Issue 2–3, pp 98–105 | Cite as

Stress-based topology optimization

  • R. J. Yang
  • C. J. Chen
Research Papers

Abstract

Previous research on topology optimization focussed primarily on global structural behaviour such as stiffness and frequencies. However, to obtain a true optimum design of a vehicle structure, stresses must be considered. The major difficulties in stress based topology optimization problems are two-fold. First, a large number of constraints must be considered, since unlike stiffness, stress is a local quantity. This problem increases the computational complexity of both the optimization and sensitivity analysis associated with the conventional topology optimization problem. The other difficulty is that since stress is highly nonlinear with respect to design variables, the move limit is essential for convergence in the optimization process. In this research, global stress functions are used to approximate local stresses. The density method is employed for solving the topology optimization problems. Three numerical examples are used for this investigation. The results show that a minimum stress design can be achieved and that a maximum stiffness design is not necessarily equivalent to a minimum stress design.

Keywords

Design Variable Topology Optimization Stress Function Structural Behaviour Topology Optimization Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baumgartner, A.; Harzheim, L.; Mattheck, C. 1992: SKO: the biological way to find an optimum structure topology.Int. J. Fatigue 14, 387–393Google Scholar
  2. Bendsøe, M.P.; Kikuchi, N. 1988: Generating optimal topologies in structural design using a homogenization method.Comp. Meth. Appl. Mech. Eng. 71, 197–224Google Scholar
  3. Cheng, G.; Jiang, Z. 1992: Study on topology optimization with stress constraints.Eng. Opt. 20, 129–148Google Scholar
  4. Díaz, A.; Kikuchi, N. 1992: Solution to shape and topology eigenvalue optimization problem using a homogenization method.Int. J. Num. Meth. Eng. 35, 1487–1502Google Scholar
  5. Gea, H.C. 1994: Topology optimization: a new micro-structure based design domain method.ASME Advances in Design Automation 2, 283–290Google Scholar
  6. Harzheim, L.; Graf, G. 1995: Optimization of engineering components with the SKO method.SAE Vehicle Struct. Mech. Conf. (held in Troy, MI), pp. 235–243Google Scholar
  7. Haug, E.J.; Choi, K.K.; Komkov, V. 1986:Design sensitivity analysis of structural systems. New York: Academic PressGoogle Scholar
  8. Jog, C.S.; Haber, R.B.; Bendsøe, M.P. 1994: Topology design with optimized, self-adaptive materials.Int. J. Num. Meth. Eng. 37, 1323–1350Google Scholar
  9. Ma, Z.D.; Kikuchi, N.; Cheng, H.C.; Hagiwara, I. 1995: Topological optimization technique for free vibration problems.Trans. ASME, J. Appl. Mech. 62, 200–207Google Scholar
  10. Mlejnek, H.P.; Schirrmacher, R. 1993: An engineer's approach to optimal material distribution and shape finding.Comp. Meth. Appl. Mech. Eng. 106, 1–26Google Scholar
  11. Park, Y.K. 1995:Extensions of optimal layout design using the homogenization method. Ph.D. Thesis, University of Michigan, Ann ArborGoogle Scholar
  12. Rozvany, G.I.N.; Bendsøe, M.P.; Kirsch, U. 1995: Layout optimization of structures.Appl. Mech. Rev. 48, 41–117Google Scholar
  13. Rozvany, G.I.N.; Zhou, M.; Birker, T. 1992: Generalized shape optimization without homogenization.Struct. Optim. 4, 250–252Google Scholar
  14. Sankaranaryanan, S.; Haftka, R.T.; Kapania, R.K. 1992: Truss topology optimization with stress and displacement constraints. In: Bendsøe, M.P.; Mota Soares, C.A. (eds.)Topology design of structures, pp. 71–78. Dordrecht: KluwerGoogle Scholar
  15. Wang, B.P.; Lu, C.M.; Yang, R.J. 1996: Optimal topology for maximum eigenvalue using density-dependent material model.37th AIAA/ASME/ASCE/AHS/ASC Structures, Struct. Dyn. Mat. Conf. (held in Salt Lake City, UT), pp. 2644–2652Google Scholar
  16. Yang, R.J.; Chahande, A.I. 1995: Automotive applications of topology optimization.Struct. Optim. 9, 245–249Google Scholar
  17. Yang, R.J.; Chuang, C.H. 1994: Optimal topology design using linear programming.Comp. & Struct. 52, 265–275Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • R. J. Yang
    • 1
  • C. J. Chen
    • 1
  1. 1.Ford Motor CompanyDearbornUSA

Personalised recommendations