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Shape Optimization under Shakedown Constraints

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Book cover Inelastic Analysis of Structures under Variable Loads

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 83))

Abstract

Based on Melan’s static shakedown theorem for linear unlimited kinematic hardening material behaviour, we formulate an integrated approach for all necessary variations within direct analysis, shakedown analysis and variational design sensitivity analysis based on convected coordinates. Using a special formulation of the optimization problem of shakedown analysis, we easily derive the necessary variations of residuals, objectives and constraints. Subsequent discretizations w.r.t. displacements and geometry using e.g. an isoparametric finite element method yield the well known tangent stiffness matrix and tangent sensitivity matrix, as well as the corresponding matrices for the variation of the Lagrange-functional. Thus, all expressions on the element level are dependent only on the nodal values of the displacements and the coordinates but not on a single design variable or the corresponding design velocity field. Remarks on the computer implementation and a numerical example show the efficiency of the proposed formulation.

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Authors and Affiliations

  1. Institute of Structural Mechanics and Computational Mechanics, University of Hannover, Appelstr. 9 A, D-30167, Hannover, Germany

    K. Wiechmann, F.-J. Barthold & E. Stein

Authors
  1. K. Wiechmann
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  2. F.-J. Barthold
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  3. E. Stein
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Editor information

Editors and Affiliations

  1. Institut für allgemeine Mechanik, Rheinisch-Westfälische Technische Hochschule Aachen, Germany

    Dieter Weichert

  2. Department of Structural Engineering, Technical University (Politecnico) of Milan, Italy

    Giulio Maier

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© 2000 Kluwer Academic Publishers

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Wiechmann, K., Barthold, FJ., Stein, E. (2000). Shape Optimization under Shakedown Constraints. In: Weichert, D., Maier, G. (eds) Inelastic Analysis of Structures under Variable Loads. Solid Mechanics and Its Applications, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9421-4_4

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  • DOI: https://doi.org/10.1007/978-94-010-9421-4_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0382-0

  • Online ISBN: 978-94-010-9421-4

  • eBook Packages: Springer Book Archive

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