Skip to main content
SpringerLink
Log in

Error analysis of refined semianalytical design sensitivities

  • Research Papers
  • Published:
Structural optimization Aims and scope Submit manuscript

Abstract

In the recent past inaccuracy problems that arise when computing shape design sensitivities by the semianalytical method have been reported. Therefore, the authors have developed a refined semianalytical method. This method is based on the fact that the contribution to the pseudo-load vector corresponding to the rigid body motions can be evaluated by exact differentiation of the rigid body modes. In the present paper the effectiveness of this refined semianalytical method is studied by means of the beam model problem. This model problem has been investigated earlier by Barthelemyet al. (1988), Barthelemy and Haftka (1988), Pedersenet al. (1989) and Olhoff and Rasmussen (1991).

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

  • Barthelemy, B.; Haftka, R.T. 1988: Accuracy analysis of the semianalytical method for shape sensitivity.AIAA Paper 88-2284, Proc. AIAA/ASME/ASCE/ASC 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, VA), pp. 562–581. Also (1990):Mech. Struct. Mach. 18, 407–432

  • Barthelemy, B.; Chon, C.T.; Haftka, R.T. 1988: Accuracy problems associated with semi-analytical derivatives of static response.Finite Elements in Analysis and Design 4, 249–265

    Google Scholar 

  • Cheng, G.; Olhoff, N. 1993: Rigid body motion test against error in semi-analytical sensitivity analysis.Struct. Optim. 46, 515–527

    Google Scholar 

  • Cheng, G.; Gu, Y.; Zhou, Y. 1989: Accuracy of semi-analytic sensitivity analysis.Finite Elements in Analysis and Design 6, 113–128

    Google Scholar 

  • Fenyes, P.; Lust, R.V. 1991: Error analysis of semianalytic displacement derivatives for shape and sizing variables.AIAA J. 29, 271–279

    Google Scholar 

  • Haftka, R.T.; Adelman, H.M. 1989: Recent developments in structural sensitivity analysis.Struct. Optim. 1, 137–151

    Google Scholar 

  • van Keulen, F.; de Boer, H. 1997: Rigorous improvement of semianalytical design sensitivities by exact differentiation of rigid body motions.Int. J. Num. Meth. Eng. (submitted)

  • Mlejnek, H.P. 1992: Accuracy of semi-analytical sensitivities and its improvement by the “natural method”.Struct. Optim. 4, 128–131

    Google Scholar 

  • Olhoff, N.; Rasmussen, J. 1991: Study of inaccuracy in semianalytical sensitivity analysis—a model problem.Struct. Optim. 3, 203–213

    Google Scholar 

  • Olhoff, N.; Rasmussen, J.; Lund, E. 1993: A method of “exact” numerical differentiation for error elimination in finite-element-based semi-analytical shape sensitivity analyses.Mech. Struct. Mach. 21, 1–66

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory for Engineering Mechanics, Delft University of Technology, Mekelweg 2, NL-2628 CD, Delft, The Netherlands

    H. de Boer & F. van Keulen

Authors
  1. H. de Boer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. van Keulen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Boer, H., van Keulen, F. Error analysis of refined semianalytical design sensitivities. Structural Optimization 14, 242–247 (1997). https://doi.org/10.1007/BF01197946

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01197946

Keywords

Search

Navigation