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Material Derivative Methods for Shape Design Sensitivity Analysis

  • Chapter
The Optimum Shape

Part of the book series: General Motors Research Laboratories Symposia Series ((RLSS))

Abstract

Use of the material derivative concept of continuum mechanics to relate variations in structural shape to measures of structural performance is reviewed. Alternate formulations of design sensitivity analysis are obtained in the form of boundary integrals and domain integrals. Theoretical implications of the resulting formulations are developed to include the dependence of performance on only normal variation of the boundary and the need for evaluation of trace operators for projection of stress and strain related quantities onto the boundary. Computational implications of shape design sensitivity formulations are investigated, including compatibility of design sensitivity analysis with finite element and boundary element methods of structural analysis, parameterization of boundary shape and parameterization of design velocity fields. Implementation of shape design sensitivity analysis using finite element computer codes is discussed. Recent numerical results are used to illustrate the accuracy that is achievable using methods for material derivative shape design sensitivity analysis.

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Authors and Affiliations

  1. Center for Computer Aided Design and Department of Mechanical Engineering, The University of Iowa, Iowa City, Iowa, USA

    E. J. Haug & K. K. Choi

Authors
  1. E. J. Haug
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  2. K. K. Choi
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Editor information

Editors and Affiliations

  1. General Motors Research Laboratories, USA

    J. A. Bennett  & M. E. Botkin  & 

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© 1986 Plenum Press, New York

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Haug, E.J., Choi, K.K. (1986). Material Derivative Methods for Shape Design Sensitivity Analysis. In: Bennett, J.A., Botkin, M.E. (eds) The Optimum Shape. General Motors Research Laboratories Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-9483-3_2

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  • DOI: https://doi.org/10.1007/978-1-4615-9483-3_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-9485-7

  • Online ISBN: 978-1-4615-9483-3

  • eBook Packages: Springer Book Archive

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