Advertisement

Structural optimization

, Volume 11, Issue 2, pp 102–112 | Cite as

Performance comparison of SAM and SQP methods for structural shape optimization

  • F. -J. Barthold
  • N. Stander
  • E. Stein
Research Papers

Abstract

This paper presents a numerical performance comparison of a modern version of the well-established sequential quadratic programming (SQP) method and the more recent spherical approximation method (SAM). The comparison is based on the application of these algorithms to examples with nonlinear objective and constraint functions, among others: weight minimization problems in structural shape optimization. The comparison shows that both the SQP and SAM-algorithms are able to converge to accurate minimum weight values. However, because of the lack of a guaranteed convergence property of the SAM method, it exhibits an inability to consistently converge to a fine tolerance. This deficiency is manifested by the appearance of small oscillations in the neighbourhood of the solution.

Keywords

Civil Engineer Approximation Method Minimization Problem Performance Comparison Quadratic Programming 
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. Arora, J.S. 1989a:Introduction to optimum design. New York: McGraw-HillGoogle Scholar
  2. Arora, J.S. 1989b: IDESIGN user's manual version 3.5.2.Technical report No. ODL-89.7, Optimal Design Laboratory, College of Engineering, The University of IowaGoogle Scholar
  3. Barthold, F.-J. 1993:Theory and computation of the analysis and optimization of isotropic, hyperelastic structures (in German). Ph.D. Dissertation, University of HannoverGoogle Scholar
  4. Becker, A. 1992:Structural optimization of stability sensitive systems by means of analytical sensitivity analysis (in German). Ph.D. Dissertation, University of HannoverGoogle Scholar
  5. Belegundu, A.D. 1985: A study of mathematical programming methods for structural optimization. Part I: theory, Part II: numerical results.Int. J. Num. Meth. Eng. 21, 1583–1623Google Scholar
  6. Bletzinger, K.U. 1990:Shape optimization of surface structures (in German). Ph.D. Dissertation, Institut für Baustatik, Univ. of StuttgartGoogle Scholar
  7. Canfield, R. 1995: A rank two Hessian matrix update for sequential quadratic approximation.Proc. 36th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf. (held in New Orleans, LA)Google Scholar
  8. De Klerk, E.; Snyman, J.A. 1994: A feasible descent cone method for linearly constrained minimization problems.Comp. & Math. Appl. 28, 33–44Google Scholar
  9. Fadel, G.M.; Riley, M.F.; Barthelemy, J.M. 1990: Two-point exponential approximation method for structural optimization.Struct. Optim. 2, 117–124Google Scholar
  10. Falk, A. 1995: Adaptive methods for shape optimization of shell structures including CAD-FEM-coupling (in German). Ph.D. Dissertation, Institut für Baumechanik u. Numerische Mechanik, University of HannoverGoogle Scholar
  11. Haftka, R.T.; Gürdal, Z. 1992:Elements of structural optimization. Boston: KluwerGoogle Scholar
  12. Haftka, R.T.; Nachlas, J.A.; Watson, L.T.; Rizzo, T.; Desai, R. 1987: Two-point constraint approximation in structural optimization.Comp. Meth. Appl. Mech. Eng. 60, 289–301Google Scholar
  13. Han, S.-P. 1976: Superlinearly convergent variable metric algorithms for general nonlinear programming problems.Math. Prog. 11, 263–282Google Scholar
  14. Han, S.-P. 1977: A globally convergent method for nonlinear programming.J. Optimiz. Theory Appl. 22, 297–309Google Scholar
  15. Hock, W.; Schittkowski, K. 1981: Test examples for nonlinear programming codes.Lecture Notes in Economics and Mathematical Systems 187. Berlin, Heidelberg, New York: SpringerGoogle Scholar
  16. Mahnken, R. 1992:Dual methods for nonlinear optimization problems in structural mechanics (in German). Ph.D. Dissertation, Institut für Baumechanik u. Numerische Mechanik, University of HannoverGoogle Scholar
  17. Powell, M.J.D. 1978a: A fast algorithm for nonlinearly constrained optimization calculations. In: Watson, G.A. (ed.)Numerical analysis.Lecture Notes in Mathematics 630. Berlin, Heidelberg, New York: SpringerGoogle Scholar
  18. Powell, M.J.D. 1978b: The convergence of variable metric methods for nonlinearly constrained optimization calculations. In Mangasarian, O.L.; Meyer, R.R.; Robinson, S.M. (eds.)Nonlinear programming 3. New York: Academic PressGoogle Scholar
  19. Prasad, B. 1983: Explicit constraint approximation forms in structural optimization. Part 1: analyses and projections.Comp. Meth. Appl. Mech. Eng. 40, 1–26Google Scholar
  20. Schittkowski, K. 1981: The nonlinear programming method of Wilson, Han and Powell with an augmented Lagrangian type line search function.Numerische Mathematik 38, 83–114Google Scholar
  21. Schittkowski, K. 1983: On the convergence of a sequential quadratic programming method with an augmented Lagrangian line search function.Optimization, Mathematische Operationsforschung und Statistik 14, 197–216Google Scholar
  22. Schittkowski, K. 1985: On the global convergence of nonlinear programming algorithms.J. Mech. Trans. Auto. Des. 107, 454–458Google Scholar
  23. Schittkowski, K. 1987: More test examples for nonlinear programming codes.Lecture Notes in Economics and Mathematical Systems 282. Berlin, Heidelberg, New York: SpringerGoogle Scholar
  24. Schittkowski, K.; Zillober, C.; Zotemantel, R. 1994: Numerical comparison of nonlinear programming algorithms for structural optimization.Struct. Optim. 7, 1–19Google Scholar
  25. Schmit, L.A.; Farshi B. 1974: Some approximation concepts for structural synthesis.AIAA J. 12, 692–699Google Scholar
  26. Schmit, L.A.; Miura, H. 1976: Approximation concepts for efficient structural synthesis.NASA CR-2552 Google Scholar
  27. Snyman, J.A.; Stander, N. 1994: A new successive approximation method for optimum structural design.AIAA J. 32, 1310–1315Google Scholar
  28. Snyman, J.A.; Stander, N. 1996: Feasible descent cone methods for inequality constrained optimization problems.Int. J. Num. Meth. Eng. (to appear)Google Scholar
  29. Stander, N.; Snyman, J.A. 1993: A new first order interior feasible direction method for structural optimization.Int. J. Num. Meth. Eng. 36, 4009–4026Google Scholar
  30. Stander, N.; Snyman, J.A.; Coster, J.E. 1995: On the robustness and efficiency of the SAM algorithm for structural optimization.Int. J. Num. Meth. Eng. 38, 119–135Google Scholar
  31. Starnes, J.H.; Haftka, R.T. 1979: Preliminary design of composite wings for buckling stress and displacement constraints.J. Aircraft 16, 564–570Google Scholar
  32. Sunar, M.; Belegundu, A.D. 1991: Trust region methods for structural optimization using exact second order sensitivity.Int. J. Numer. Meth. Eng. 32, 275–293Google Scholar
  33. Thanedar, P.B.; Arora, J.S.; Tseng, C.H.; Lim, O.K.; Park, G.J. 1986: Performance of some SQP algorithms on structural design problems.Int. J. Numer. Meth. Eng. 23, 2187–2203Google Scholar
  34. Tseng, C.H.; Arora, J.S. 1988: On implementation of computational algorithms for optimal design 1: preliminary investigation and 2: extensive numerical investigation.Int. J. Numer. Meth. Eng. 26, 1383–1402Google Scholar
  35. Venkayya, V.B.; Khot, N.S.; Reddy, V.S. 1968: Energy distribution in an optimum structural design.AFFDL-TR-68-156 Google Scholar
  36. Wilson, R.B. 1963:A simplical method for concave programming. Ph.D. Dissertation, Harvard University, Cambridge, Mass., USAGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • F. -J. Barthold
    • 1
  • N. Stander
    • 1
  • E. Stein
    • 1
  1. 1.Institut für Baumechanik und Numerische MechanikUniversität HannoverHannoverGermany

Personalised recommendations