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Optimal Structural Design in Nonsmooth Mechanics

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Multilevel Optimization: Algorithms and Applications

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 20))

Abstract

Optimal structural design problems concern with the choice of the design parameters (material variables, shapes etc) of a structure such as to make optimal certain response variables; this task is measured by an appropriate cost or gain function. They are mathematical programs with equilibrium constraints. The use of bilevel optimization techniques permit us to separate the optimal design problem and the structural analysis problem in two levels (subproblems) and, accordingly, allow for the use of existing methods and software for the solution of each one subproblem. In particular the utilisation of the powerful finite element analysis software is indispensable, since it permits the effective treatment of large scale problems.

Here the optimal structural design problem for nonsmooth mechanics’ structures is studied. All structures which involve non-differentiable potential energy functions and / or inequalities in their definition lead to nonsmooth mechanics problems. They are highly nonlinear problems which include, among others, frictionless and frictional unilateral contact effects, elastoplasticity etc. The structural analysis problem leads to nonsmooth potential energy minimization problems (or to substationarity problems in the case of nonconvex potentials). The nondifferentiability and the possible nonconvexity at the structural analysis level must be taken into account for the solution of the optimal design problem. In this chapter bilevel optimization algorithms for the solution of this problem will be investigated. Two model problems for which appropriate modelling techniques have been formulated and studied are presented here. They are solved by using previously published results and bilevel algorithms based on a coupling of nonsmooth optimization techniques with finite element modelling. The general problem is open for further research, a fact which is hoped to stimulate people working on multilevel and global optimization to contribute in this area.

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Author information

Authors and Affiliations

  1. Institute of Applied Mechanics, Carolo Wilhelmina TU Braunschweig, Germany

    Georgios E. Stavroulakis

  2. Department C for Mathematics, RWTH Aachen, D-52056, Aachen, Germany

    Harald Günzel

Authors
  1. Georgios E. Stavroulakis
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  2. Harald Günzel
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Editor information

Editors and Affiliations

  1. Division of Optimization, Department of Mathematics, Linköping Institute of Technology, Linköping, Sweden

    Athanasios Migdalas  & Peter Värbrand  & 

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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© 1998 Kluwer Academic Publishers

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Stavroulakis, G.E., Günzel, H. (1998). Optimal Structural Design in Nonsmooth Mechanics. In: Migdalas, A., Pardalos, P.M., Värbrand, P. (eds) Multilevel Optimization: Algorithms and Applications. Nonconvex Optimization and Its Applications, vol 20. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0307-7_4

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  • DOI: https://doi.org/10.1007/978-1-4613-0307-7_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7989-8

  • Online ISBN: 978-1-4613-0307-7

  • eBook Packages: Springer Book Archive

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