Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Multiparametric shape optimal design of disks

  • 49 Accesses

  • 1 Citations


The external boundary of a structure described by a set of design parameters undergoes shape modification. Arbitrary stress, strain and displacement functionals are defined within the domain of the structure and its first- and second-order sensitivities with respect to varying structural shape are discussed. The optimal shape design problem is then formulated and solved using the first- and second-order sensitivity information. The iterative analysis-redesign algorithm is formulated using the finite element method. Some illustrative examples are included.

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


  1. Banichuk, N.V. 1975: On a variational problem with unknown boundaries and determination of the optimal shapes of elastic bodies.PMM 39, 1082–1092

  2. Banichuk, N.V.; Bielskij, V.G.; Kobielew, V.V. 1984: Optimization for the theory elasticity problems with unknown boundaries.MTT Mech. Solids 3, 46–52

  3. Banichuk, N.W. 1990:Introduction to optimal design. Berlin, Heidelberg, New York: Springer

  4. Brown, P.M.; Ang, A.H.S. 1966: Structural optimization by nonlinear programming.J. Struct. Div. ASCE 92, 319–340

  5. Cantin, G.; Loubignac, G.; Touzot, G. 1978: An iterative algorithm to build continuous stress and displacement solutions.Int. J. Num. Meth. Eng. 12, 1493–1506

  6. Choi, K.K.; Santos, J.L.T.; Frederick, M.C. 1987: Implementation of design sensitivity analysis with existing finite element codes.ASME J. Mech. Trans. Auto.

  7. Choi, K.K.; Seong, H.G. 1986: A domain method for shape design sensitivity analysis of build-up structures.Comp. Meth. Appl. Mech. Eng. 57, 1–15

  8. Dems, K. 1981: Optimal shape design of loaded boundaries.Arch. Mech. 33, 2, 243–260

  9. Dems, K. 1991: First- and second-order shape sensitivity analysis of structures.Struct. Optim. 3, 79–88

  10. Dems, K.; Haftka, R.T. 1988–89: Two approaches to sensitivity analysis for shape variation of structures.Mech. Struct. Mach. 16, 501–522

  11. Dems, K.; Korycki, R. 1994: Second-order sensitivities with respect to shape of loaded and supported structural boundaries.Publicationsbook of the Łodź Technical University (in print)

  12. Dems, K.; Mróz, Z. 1983: Variational approach by means of adjoint systems to structural optimization and sensitivity analysis -1. Variation of material parameters within fixed domain.Int. J. Solids & Struct. 19, 677–692

  13. Dems, K.; Mróz, Z. 1984: Variational approach by means of adjoint systems to structural optimization and sensitivity analysis -2. Structure shape variation.Int. J. Solids & Struct. 20, 527–552

  14. Dems, K.; Mróz, Z. 1985: Variational approach to first- and second-order sensitivity analysis of elastic structures.Int. J. Num. Meth. Eng. 21, 637–661

  15. Eschenauer, H.A.; Koski, J.; Osyczka, A. 1990:Multicriteria design optimization. Berlin, Heidelberg, New York: Springer

  16. Fuji, N. (ed.) 1986: Domain optimization problems with a boundary value problem as a constraint in control of distributed parameter systems.Proc. 4th IFAC Symp. (held in Los Angeles). Oxford: Pergamon Press

  17. Haftka, R.T. 1982: Second-order sensitivity derivatives in structural analysis.AIAA J. 20, 1765–1786

  18. Haftka, R.T.; Mróz, Z. 1986: First- and second-order sensitivity analysis of linear and non-linear structures.AIAA J. 24, 1187–1192

  19. Haug, E.J.; Choi, K.K.; Komkov, V. 1986:Design sensitivity analysis of structural systems. New York: Academic Press

  20. Kelly, D.W.; Stafford, R.O. 1977: A review of techniques for automated structural design.Comp. Meth. Appl. Mech. Eng. 12, 219–242

  21. Olhoff, N.; Rasmussen, J. 1990: Method of error elimination for a class of semi-analytical sensitivity analysis problems. In: Eschenauer, H.A.; Mattheck, C.; Olhoff, N. (eds.)Engineering optimization in design processes, pp. 193–200. Berlin, Heidelberg, New York: Springer

  22. Olhoff, N.; Taylor, J.F. 1983: On structural optimization.J. Appl. Mech. 50, 114–122

  23. Pedersen, P.; Cheng, G.; Rasmussen, J. 1989: On accuracy problems for semi-analytical sensitivity analyses.Mech. Struct. Mach. 17, 373–384

  24. Rozvany, G.I.N. 1989:Structural design via optimality criteria. Dodrecht: Kluwer

  25. Yang, R.J.; Choi, K.K. 1985: Accuracy of finite element based shape design sensitivity analysis.J. Struct. Mech. 13, 223–239

  26. Zolezio, J.P. 1981: The material derivative (or speed) method for shape optimization. In: Haug, E.J. and Cea, J. (eds.)Optimization of distributed parameter structures, pp. 1089–1157. Alphen aan den Rijn: Sijthoff and Noordhoff

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Korycki, R. Multiparametric shape optimal design of disks. Structural Optimization 9, 25–32 (1995). https://doi.org/10.1007/BF01742641

Download citation


  • Finite Element Method
  • Civil Engineer
  • Optimal Design
  • Design Parameter
  • Design Problem