Skip to main content
SpringerLink
Log in

Nonparametric gradient-less shape optimization for real-world applications

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

A nonparametric gradient-less shape optimization approach for finite element stress minimization problems is presented. The shape optimization algorithm is based on optimality criteria, which leads to a robust and fast convergence independent of the number of design variables. Sensitivity information of the objective function and constraints are not required, which results in superior performance and offers the possibility to solve the structural analysis task using fast and reliable industry standard finite element solvers such as ABAQUS, ANSYS, I-DEAS, MARC, NASTRAN or PERMAS. The approach has been successfully extended to complex nonlinear problems including material, boundary and geometric nonlinear behavior. The nonparametric geometry representation creates a complete design space for the optimization problem, which includes all possible solutions for the finite element discretization. The approach is available within the optimization system TOSCA and has been used successfully for real-world optimization problems in industry for several years. The approach is compared to other approaches and the benefits and restrictions are highlighted. Several academic and real-world examples are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bakhtiary-96 Bakhtiary N and other (1996) A new approach for sizing, shape and topology optimization. SAE International Congress and Exposition, Detroit/Michigan

  2. Banichuk-95 Banichuk NV, Barthold F-J, Falk A, Stein E (1995) Mesh refinement for shape optimization. Struct Optim 9:46–51

    Google Scholar 

  3. Barthelemy-93 Barthelemy J-FM, Haftka RT (1993) Approximation concepts for optimum structural design—a review. Struct Optim 5:129–144

    Google Scholar 

  4. Baud-34 Baud RV (1934) Fillet profiles for constant stress. Prod Eng 5(4):133–134

    Google Scholar 

  5. Belegundu-88 Belegundu AD, Rajan SD (1988) A shape optimization approach based on natural design variables and shape functions. Comput Methods Appl Mech Eng 66:87–106

    Google Scholar 

  6. Bennett-85 Bennett JA, Botkin ME (1985) Structural shape optimization with geometric description and adaptive mesh generation. AIAA J 23:458–464

    Google Scholar 

  7. Bletzinger-90 Bletzinger K-U (1990) Formoptimierung von Flächentragwerken. Institut für Baustatik, University of Stuttgart, Dissertation

  8. Bletzinger-91 Bletzinger K-U, Kimmich S, Ramm E (1991) Efficient modeling in shape optimal design. Comut Syst Eng 2:483–495

    Google Scholar 

  9. Braibant-84 Braibant V, Fleury C (1984) Shape optimal design using B-splines. Comput Methods Appl Mech Eng 44:247–267

    Google Scholar 

  10. Chen-93 Chen JL, Tsai WC (1993) Shape optimzation using simulated biological growth approaches. AIAA J 31:2143–2147

    Google Scholar 

  11. Cheng-93-2 Cheng G, Olhoff N (1993) Rigid body motion test against error in semi-analytical sensitivity analysis. Comput Struct 46:515–527

    Google Scholar 

  12. Cherepanov-74 Cherepanov GP (1974) Inverse problems of the plane theory of elasticity. J Appl Math Mech 39(6):1082–1092

    Google Scholar 

  13. Cohn-94 Cohn MZ (1994) Theory and practice of structural optimization. Struct Optim 1994:20–31

  14. Ding-86 Ding Y (1986) Shape optimization of structures: a literature survey. Comput Struct 24:985–1004

    Google Scholar 

  15. Falk-99 Falk A, Barthold F-J, Stein E (1999) A hierarchical design concept for shape optimization based on the interaction of CAGD and FEM. Struct Optim 18:12–23

    Google Scholar 

  16. Fancello-95 Fancello EA, Haslinger J, Feijóo RA (1995) Numerical comparison between two cost functions in contact shape optimization. Struct Optim 9:57–68

    Google Scholar 

  17. Gellatly-76 Gellatly RA, Dupree DM (1976) Examples of computer-aided optimal design of structures. 10th IABSE Congress, 77–105, Tokyo

  18. Goldberg-89 Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison–Wesley, Boston

  19. Haftka-86 Haftka RT, Grandhi RV (1986) Structural shape optimization—a survey. Comput Methods Appl Mech Eng 57:517–522

    Google Scholar 

  20. Iancu-90 Iancu G (1990) Spannungskonzentrationsminimierung dreidimensionaler elastischer Kontinua mit der FEM. University of Karlsruhe, Dissertation

  21. Imam-82 Imam MH (1982) Three-dimensional shape optimization. Int J Numer Methods Eng 18:661–673

    Google Scholar 

  22. Kikuchi-86 Kikuchi N, Chung KY, Torigaki T, Taylor JE (1986) Adaptive finite element methods for shape optimization of linearly elastic structures. Comput Methods Appl Mech Eng 57:67–89

    Google Scholar 

  23. Kirsch-93 Kirsch U (1993) Structural optimization: fundamentals and applications. Springer, Berlin Heidelberg New York

  24. Mattheck-90 Mattheck C, Burkardt S (1990) A new method of structural shape optimization based on biological growth. Int J Fatigue 12:185–190

    Google Scholar 

  25. Meske-02 Meske R, Mulfinger F, Warmuth O (2002) Topology and shape optimization of components and systems with contact boundary conditions. In: Modellieren von Baugruppen und Verbindungen für FE-Berechnungen, Wiesbaden, April 2002, NAFEMS

  26. Neuber-57 Neuber H (1957) Kerbspannungslehre, Grundlagen für genaue Festigkeitsberechnung. 2nd edn, Springer, Berlin Heidelberg New York

  27. Olhoff-93 Olhoff N, Rasmussen J, Lund E (1993) Method of exact numerical differentiation for error elimination in finite element based semi-analytical shape sensitivity analysis. Mech Struct Mach 21:1–66

    Google Scholar 

  28. Paczelt-94 Páczelt L, Szabó T (1994) Optimal shape design for contact problems. Struct Optim 7:66–75

    Google Scholar 

  29. Pedersen-00 Pedersen P (2000) On optimal shape in materials and structures. Struct Multidisc Optim 19:169–182

    Google Scholar 

  30. Rechenberg-89 Rechenberg I (1989) Evolution strategy: nature’s way of optimization. In: Bergmann H (ed) Optimization: methods and applications, possibilities and limitations. Springer, Berlin Heidelberg New York, pp. 106–126

  31. Sauter-91 Sauter J (1991) CAOS oder die Suche nach der optimalen Bauteilform durch eine effiziente Gestaltoptimierungsstrategie. XX. Internationaler Finite Elemente Kongress, Baden-Baden, November 1991

  32. Schittkowski-94 Schittkowski K, Zillober C, Zotemantel R (1994) Numerical comparison on nonlinear programming algorithms for structural optimization. Struct Optim 7:1–28

    Google Scholar 

  33. Schleupen-00 Schleupen A, Maute K, Ramm E (2000) Adaptive FE-procedures in shape optimization. Struct Multidisc Optim 19:282–302

    Google Scholar 

  34. Schnack-77 Schnack E (1977) Ein Iterationsverfahren zur Optimierung von Spannungskonzentrationen. University of Kaiserslautern, Habilitation

  35. Schnack-79 Schnack E (1979) An optimization procedure for stress concentrations by the finite element technique. Int J Numer Math Eng 14:115–124

    Google Scholar 

  36. Schnack-80 Schnack E (1980) Optimierung von Spannungskonzentrationen bei Viellastbeanspruchung. ZAMM 60:151–152

    Google Scholar 

  37. Schnack-86 Schnack E, Spörl U (1986) A mechanical dynamic programming algorithm for structure optimization. Int J Numer Math Eng 23:1985–2004

    Google Scholar 

  38. Schnack-88 Schnack E, Spörl U, Iancu G (1988) Gradientless shape optimization with FEM. VDI Forschungsheft, 647

  39. Spoerl-85 Spörl U (1985) Spannungsoptimale Auslegung elastischer Strukturen. University of Karlsruhe, Dissertation

  40. Vanderplaats-84 Vanderplaats G (1984) Numerical optimization techniques for engineering design. McGraw–Hill, New York

  41. Woon-01 Woon SY, Querin OM, Steven GP (2001) Structural application of a shape optimization method based on a genetic algorithm. Struct Multidisc Optim 22:57–64

    Google Scholar 

  42. Zhang-92 Zhang S, Belegundu AD (1992) A systematic approach for generating velocity fields in shape optimization. Struct Optim 5:84–94

    Google Scholar 

  43. Zhang-95 Zhang W-H, Beckers P, Fleury C (1995) A unified parametric design approach to structural shape optimization. Int J Numer Methods Eng 38:2283–2292

    Google Scholar 

  44. Zienkiewicz-73 Zienkiewicz OC, Campbell JS (1973) Shape optimization and sequential linear programming. In: Gallagher RH, Zienkiewicz OC (eds) Optimum structural design: theory and applications. Wiley, London, pp. 109–126

Download references

Author information

Authors and Affiliations

  1. FE-DESIGN GmbH, Haid-und-Neu Str. 7, 76131, Karlsruhe, Germany

    R. Meske & J. Sauter

  2. University of Karlsruhe, Kaiserstr. 12, 76131, Karlsruhe, Germany

    E. Schnack

Authors
  1. R. Meske
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Sauter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Schnack
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Meske.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Meske, R., Sauter, J. & Schnack, E. Nonparametric gradient-less shape optimization for real-world applications. Struct Multidisc Optim 30, 201–218 (2005). https://doi.org/10.1007/s00158-005-0518-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-005-0518-0

Keywords

Search

Navigation