Differentiability of strongly singular BIE formulations with respect to boundary perturbations

  • Marc Bonnet
Conference paper


In e.g. shape design analysis, inverse problems or fracture mechanics, one is often faced with the need of computing sensitivities of functional or physical variables with respect to perturbations of the shape of the geometrical domain Ω, under study. This goal is often achieved using analytical material differentiation followed by discretization, in the form of either the adjoint variable approach or the direct differentiation. In a BEM context, the latter is based on material differentiation of the relevant governing BIE formulation, so that a governing BIE for the field sensitivities is available.


Boundary Element Method Material Differentiation Geometrical Transformation Material Derivative Boundary Perturbation 
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  1. [1]
    Barone M.R., Yang R.J. — A Boundary Element Approach for Recovery of Shape Sensitivities in Three-dimensional Elastic Solids. Comp. Meth. in Appl. Mech. & Engng., 74, pp. 69–82, 1989. zbMATHCrossRefGoogle Scholar
  2. [2]
    Mellings S.C., Aliabadi M.H. — Three-dimensional flaw identification using sensitivity analysis. Boundary Element Method XVI, pp. 149–156, Comp. Mech. Publ. Southampton, 1994. Google Scholar
  3. [3]
    Bui H.D. — Some remarks about the formulation of three-dimensional ther-moelastoplastic problems by integral equations. Int. J. Solids Struct., 14, pp. 935-, 1978. zbMATHCrossRefGoogle Scholar
  4. [4]
    Petryk H., Mroz Z. — Time derivatives of integrals and functionals defined on varying volume and surface domains. Arch. Mech., 38, pp. 694–724, 1986. MathSciNetGoogle Scholar
  5. [5]
    Bonnet M. — Regularized BIE formulations for first- and second-order shape sensitivity of elastic fields. Special issue of Computers and Structures, (S. Saigal, guest editor.), to appear, 1995.Google Scholar
  6. [6]
    Guiggiani M. & Gigante A. — A general algorithm for multidimensional Cauchy principal value integrals in the boundary element method. A S ME J. Appl Mech., 57, pp. 906–915, 1990. MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    Zhang Q., Mukherjee S. — Second-order design sensitivity analysis for linear elastic problems by the derivative boundary element method. Comp. Meth. in Appl. Mech. & Engng., 86, pp. 321–335, 1991. zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Marc Bonnet
    • 1
  1. 1.Laboratoire de Mécanique des Solides (URA CNRS 317)Ecole PolytechniquePalaiseauFrance

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