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Topological sensitivity derivative and finite topology modifications: application to optimization of plates in bending

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Abstract

The concept of topological sensitivity derivative is introduced and applied to study the problem of optimal design of structures. It is assumed, that virtual topology variation is described by topological parameters. The topological derivative provides the gradients of objective functional and constraints with respect to these parameters. This derivative enables formulation of the conditions of topology transformation. In this paper formulas for the topological sensitivity derivative for bending plates are derived. Next, the topological derivative is used in the optimization process in order to formulate conditions of finite topology modifications and in order to localize positions of the modifications. In the case of plates they are related to introduction of holes and introduction of stiffeners. The theoretical considerations are illustrated by some numerical examples.

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Authors and Affiliations

  1. Faculty of Management and Computer Modelling, Kielce University of Technology, Kielce, Poland

    Dariusz Bojczuk

  2. Institute of Fundamental Technological Research, Warsaw, Poland

    Zenon Mróz

Authors
  1. Dariusz Bojczuk
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  2. Zenon Mróz
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Correspondence to Dariusz Bojczuk.

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Bojczuk, D., Mróz, Z. Topological sensitivity derivative and finite topology modifications: application to optimization of plates in bending. Struct Multidisc Optim 39, 1–15 (2009). https://doi.org/10.1007/s00158-008-0333-5

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  • DOI: https://doi.org/10.1007/s00158-008-0333-5

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