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Structural optimization

, Volume 11, Issue 1–2, pp 29–42 | Cite as

A continuum mechanical-based formulation of the variational sensitivity analysis in structural optimization. Part I: analysis

  • F. -J. Barthold
  • E. Stein
Research Papers

Abstract

A variational formulation of shape design sensitivity analysis is outlined, starting from a differential geometry-based representation of continuum mechanics.

A rigorous analysis using convected curvilinear coordinates yields a decomposition of all continuum mechanical functions into independent geometry and displacement mappings. Using this representation of geometry and displacements defined on a fixed parameter space, their influence on physical quantities can easily be separated. Consequently, the variations of continuum mechanical quantities with respect to either geometry or displacements can be performed similarly using the well-known linearization techniques in nonlinear mechanics.

The proposed methodology for performing variational design sensitivity analysis is formulated for general nonlinear hyperelastic material behaviour using either the Lagrangian or Eulerian description. The differences and similarities of the formulation presented compared with the material derivative approach and the domain parametrization approach are highlighted and discussed.

Keywords

Variational Design Displacement Mapping Domain Parametrization Shape Design Nonlinear Mechanic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • F. -J. Barthold
    • 1
  • E. Stein
    • 1
  1. 1.Institute for Structural Mechanics and Computational MechanicsUniversity of HannoverHannoverGermany

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