Skip to main content
SpringerLink
Log in

Material derivative and control volume approaches to shape sensitivity analysis of nonlinear transient thermal problems

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

Abstract

The problem of the shape design sensitivity of nonlinear transient thermal systems is considered. The nonlinear shape design sensitivity is formulated by using a weighted residual method employing the continuum description. Both material derivative and control volume approaches for structural shape design sensitivity analysis are presented, analysed and compared. It is shown that the final design sensitivity expressions for the two approaches are theoretically equivalent.

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

  • Adelman, H.M.; Haftka, R.T. 1986: Sensitivity analysis of discrete structural systems.AIAA J. 24, 823–832

    Google Scholar 

  • Arora, J.S.; Cardoso, J.B. 1992: Variational principle for shape design sensitivity analysis.AIAA J. 30, 538–547

    Google Scholar 

  • Arora, J.S.; Lee, T.H.; Cardoso, J.B. 1992: Structural shape sensitivity analysis: relationship between material derivative and control volume approaches.AIAA J. 30, 1638–1648

    Google Scholar 

  • Belegundu, A.D.; Rajan, S.D. 1988: A shape optimization approach based on natural design variables and shape functions.Comp. Meth. Appl. Mech. Engng. 66, 87–106

    Google Scholar 

  • Choi, K.K.; Haug, E.J. 1983: Shape design sensitivity analysis of elastic structures.J. Struct. Mech. 11, 231–269

    Google Scholar 

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

    Google Scholar 

  • Dems, K. 1987: Sensitivity analysis in thermal problems — II: structural shape variation.J. Thermal Stresses 10, 1–16

    Google Scholar 

  • Dems, K.; Haftka, R.T. 1989: Two approaches to sensitivity analysis for shape variation of structures.Mech. Struct. Mach. 16, 501–522

    Google Scholar 

  • Dems, K.; Mróz, Z. 1985: Variational approach to first and secondorder sensitivity analysis.Int. J. Num. Meth. Eng. 21, 637–646

    Google Scholar 

  • Haftka, R.T.; Adelman, H.M. 1989: Recent developments in structural sensitivity analysis.Struct. Optim. 1, 137–152

    Google Scholar 

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

    Google Scholar 

  • Hou, J.W.; Chen, J.L.; Sheen, J.S. 1986: Computational method for optimization of structural shapes.AIAA J. 24, 1005–1012

    Google Scholar 

  • Kleiber, M.; Slużalec, A. 1995: Parameter sensitivity in nonlinear transient thermal problems.Comp. Assisted Mech. & Eng. Sci. (accepted)

  • Kosiński W. 1986:Field singularities and wave analysis in continuum mechanics. New York: Halsted Press

    Google Scholar 

  • Malvern, L.E. 1969:Introduction to the mechanics of a continuous medium. Englewood Cliffs, NJ: Prentice-Hall

    Google Scholar 

  • Meric, R.A. 1988: Shape design sensitivity analysis for nonlinear anisotropic heat conducting solids and shape optimization by the BEM.Int. J. Num. Meth. Eng. 26, 109–120

    Google Scholar 

  • Park, C.W.; Yoo, Y.M. 1988: Shape design sensitivity analysis of a two-dimensional heat transfer system using the boundary element method.Comp. & Struct. 28, 543–550

    Google Scholar 

  • Seong, H.G.; Choi, K.K. 1987: Boundary-layer approach to shape design sensitivity analysis.Mech. Struct. Mach. 15, 241–267

    Google Scholar 

  • Slużalec, A.; Kleiber, M. 1995: Shape sensitivity analysis for nonlinear steady-state heat conduction problems.Int. J. Heat and Mass Transfer (accepted)

  • Tortorelli, D.A.; Haber, R.B. 1989: First-order design sensitivity for transient conduction problems by an adjoint method.Int. J. Num. Meth. Eng. 28, 733–752

    Google Scholar 

  • Tortorelli, D.A.; Haber, R.B.; Lu, S.C.-Y. 1989: Design sensitivity analysis for nonlinear thermal systems.Comp. Meth. Appl. Mech. Eng. 77, 61–77

    Google Scholar 

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

    Google Scholar 

  • Yao, T.M.; Choi, K.K. 1989: 3-D shape optimal design and automatic finite element regridding.Int. J. Num. Meth. Engng. 28, 369–384

    Google Scholar 

  • Zolesio, J.P. 1981: the material derivative (or speed) method for shape optimization. In: Haug, E.J.; Cea, J. (eds)Optimization of distributed parameter structures. Sijthoff & Noordhoff

Download references

Author information

Authors and Affiliations

  1. Institute of Fundamental Technological Research, Warsaw, Poland

    M. Kleiber

  2. Technical University of Częstochowa, Częstochowa, Poland

    A. Slużalec

Authors
  1. M. Kleiber
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Slużalec
    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

Kleiber, M., Slużalec, A. Material derivative and control volume approaches to shape sensitivity analysis of nonlinear transient thermal problems. Structural Optimization 11, 56–63 (1996). https://doi.org/10.1007/BF01279656

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01279656

Keywords

Search

Navigation