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Shape Design Sensitivity Analysis Using Boundary Integral Equation for Potential Problems

  • B. M. Kwak
  • J. H. Choi
Part of the NATO ASI Series book series (volume 27)

Abstract

A general method for shape design sensitivity analysis as applied to potential problems is developed with the standard direct boundary integral equation (BIE) formulation. The material derivative concept and adjoint variable method are employed to obtain an explicit expression for the variation of the performance functional in terms of the boundary shape variation. The adjoint problem defined in the present method takes a form of the indirect BIE. This adjoint problem can be solved using the same direct BIE of the original problem with a different set of boundary values, which brings about computational simplicity. The accuracy of the sensitivity formula is studied with a seepage problem. The detailed derivation of the formulas for general elliptic problems and a more elaborate numerical scheme will be described elsewhere.

Keywords

Free Boundary Boundary Element Method Boundary Integral Equation Adjoint System Adjoint Problem 
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References

  1. 1.
    P. K. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Science, McGraw-Hill, 1981MATHGoogle Scholar
  2. 2.
    J. P. Zolesio, The Material Derivative Method for Shape Optimization, in Optimization of Distributed Parameter Structures (E.J. Haug & J. Cea, eds.) Sijthoff & Noordhoff, Alphen aan den Rijn, Netherlands, 1981Google Scholar
  3. 3.
    K. K. Choi and E. J. Haug, Shape Design Sensitivity Analysis of Elastic Structures, J. Struct. Mech. 11: 231 - 269 (1983)MathSciNetCrossRefGoogle Scholar
  4. 4.
    J. A. Liggett and P. L-F. Liu, The Boundary Integral Equation Method for Porous Media Flow, George Allen & Unwin, 1983MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • B. M. Kwak
    • 1
  • J. H. Choi
    • 1
  1. 1.Department of Mechanical EngineeringKorea Advanced Institute of Science and TechnologySeoulKorea

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