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Structural optimization

, Volume 6, Issue 1, pp 7–14 | Cite as

Multiparameter structural optimization using FEM and multipoint explicit approximations

  • V. V. Toropov
  • A. A. Filatov
  • A. A. Polynkin
Technical Papers

Abstract

A unified approach to various problems of structural optimization, based on approximation concepts, is presented. The approach is concerned with the development of the iterative technique, which uses in each iteration the information gained at several previous design points (multipoint approximations) in order to better fit constraints and/or objective functions and to reduce the total number of FE analyses needed to solve the optimization problem. In each iteration, the subregion of the initial region in the space of design variables, defined by move limits, is chosen. In this subregion, several points (designs) are selected, for which response analyses and design sensitivity analyses are carried out using FEM. The explicit expressions are formulated using the weighted least-squares method. The explicit expressions obtained then replace initial problem functions. They are used as functions of a particular mathematical programming problem. Several particular forms of the explicit expressions are considered. The basic features of the presented approximations are shown by means of classical test examples, and the method is compared with other optimization techniques.

Keywords

Design Variable Explicit Expression Structural Optimization Design Point Move Limit 
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.

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References

  1. Barthelemy, B.; Haftka, R.T. 1988: Accuracy analysis of the semi-analytical method for shape sensitivity calculation.Proc. AIAA/ASME/ASCE/AHS/ASC 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, VA), Part 1, pp. 572–581Google Scholar
  2. Brown, R.T.; Nachlas, J.A. 1981: Structural optimization of laminated conical shells. In: Marshall, I.H. (ed.)Composite structures, pp. 144–157. Amsterdam: ElsevierGoogle Scholar
  3. Draper, N.R.; Smith, H. 1981:Applied regression analysis (2nd ed.). New York: John Wiley & SonsGoogle Scholar
  4. Fadel, G.M.; Riley, M.F.; Barthelemy, J.M. 1990: Two point exponential approximation method for structural optimization.Struct. Optim. 2, 117–124Google Scholar
  5. Fleury, C. 1989: First and second order convex approximation strategies in structural optimization.Struct. Optim. 1, 3–10Google Scholar
  6. Fleury, C. 1989: CONLIN: An efficient dual optimizer based on convex approximation concepts.Struct. Optim. 1, 81–89Google Scholar
  7. Fleury, C.; Braibant, V. 1986: Structural optimization: a new dual method using mixed variables.Int. J. Num. Meth. Eng. 23, 409–428Google Scholar
  8. Haftka, R.T.; Nachlas, J.A.; Watson, L.T.; Rizzo, T.; Desai, R. 1987: Two-point constraint approximation in structural optimization.Comp. Meth. Appl. Eng. 60, 289–301Google Scholar
  9. Ljung, L. 1987:Systems identification: theory for the user. Englewood Cliffs: Prentice HallGoogle Scholar
  10. Malkov, V.P.; Toropov, V.V.; Filatov, A.A. 1982: Simulation approach to optimization of deformable systems.Applied problems of strength and plasticity, pp. 62–69. Gorky University (in Russian)Google Scholar
  11. Malkov, V.P.; Toropov, V.V. 1990: Simulation approach to structural optimization using design sensitivity analysis. In: Eschenauer, H.A.; Mattheck, C.; Olhoff, N. (eds.)Engineering optimization in design processes, pp. 225–231. Berlin, Heidelberg, New York: SpringerGoogle Scholar
  12. Morozov, V.D. 1987: Optimization of elastic structures based on approximation by homogeneous functions. In:Applied problems of strength and plasticity, pp. 9–21. Gorky University (in Russian)Google Scholar
  13. Müller, G.; Tiefenthaler, P. 1990: Design optimization with a commercial finite element program. In: Eschenauer, H.A.; Mattheck, C.; Olhoff, N. (eds.)Engineering optimization in design processes, pp. 201–210. Berlin, Heidelberg, New York: SpringerGoogle Scholar
  14. Pedersen, P. 1981: The integrated approach of FEM-SLP for solving problems of optimal design. In: Haug, E.J.; Cea, J. (eds.)Optimization of distributed parameter structures, pp. 739–756. Amsterdam: Sijthoff and NoordhoffGoogle Scholar
  15. Pedersen, P.; Cheng, G.; Rasmussen, J. 1989: On accuracy problems for semi-analytical sensitivity analysis.Mech. Struct. Mach. 17, 373–384Google Scholar
  16. Prasad, B. 1984: Novel concepts for constraint treatment and approximations in efficient structural synthesis.AIAA J. 22, 957–966Google Scholar
  17. Rasmussen, J. 1990: Structural optimization by accumulated function approximation.Int. J. Num. Meth. Eng. (submitted)Google Scholar
  18. Schmit, L.A.; Farshi, B. 1974: Some approximation concepts for structural synthesis.AIAA J. 12, 692–699Google Scholar
  19. Schmit, L.A.; Fleury, C. 1980: Structural synthesis by combining approximation concepts and dual methods.AIAA J. 18, 1252–1260Google Scholar
  20. Schoofs, A.J.G. 1987:Experimental design and structural optimization. Doctoral Dissertation, Technical University of EindhovenGoogle Scholar
  21. Svanberg, K. 1987: The method of moving asymptotes — a new method for structural optimization.Int. J. Num. Meth. Eng. 24, 359–373Google Scholar
  22. Toropov, V.V. 1989: Simulation approach to structural optimization.Struct. Optim. 1, 37–46Google Scholar
  23. Vanderplaats, G.N. 1979: Efficient algorithm for numerical airfoil optimization.AIAA J. Aircaft 16, 842–847Google Scholar
  24. Vanderplaats, G.N. 1989: Effective use of numerical optimization in structural design.Finite Elements in Analysis and Design 6, 97–112Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • V. V. Toropov
    • 1
  • A. A. Filatov
    • 1
  • A. A. Polynkin
    • 1
  1. 1.Department of Solid MechanicsNizhny Novgorod UniversityNizhnyRussia

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