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Simultaneous topology optimization and proportional actuators localization

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Abstract

In this paper we consider the classical minimum compliance topology optimization in linear elasticity. In our approach, the objective is to minimize a cost functional that comprises the work of applied body and traction forces obtaining simultaneously the optimal topology and the optimal localization for proportional actuators on the concerning structural domain. A proportional actuator is considered as a spring and one of the objectives is to obtain the optimal local to couple it on the structure. The problem is treated as a topology optimization problem where a given cost functional must be minimized under suitable constraints for external forces, control energy, volume restriction and a set of project variables. The topology optimization procedure here performed uses the solid isotropic material with penalization approach, based on the concept of optimizing the material distribution. The solution of the optimization problem is obtained by using a sequential linear programming and the finite element method is used to discretize the design domain. Several numerical examples are presented showing the effectiveness of the proposed approach.

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Acknowledgments

The author L. S. Fernandez acknowledges the financial support of CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), Brazil.

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Authors and Affiliations

  1. Programa de Pós-Graduação em Modelagem Computacional, Laboratório Nacional de Computação Científica LNCC/MCTI, Av. Getúlio Vargas 333, Petrópolis, RJ, 25651-075, Brazil

    Lucas dos Santos Fernandez

  2. Departamento de Matemática e Estatística, Instituto de Física e Matemática, Universidade Federal de Pelotas UFPel, Campus Universitário 354, Pelotas, RS, 96010-900, Brazil

    Alexandre Molter

  3. Centro de Ciências Físicas e Matemáticas, Universidade Federal de Santa Catarina UFSC, Campus Universitário Trindade, Florianópolis, SC, 88040-900, Brazil

    Fabio Silva Botelho

Authors
  1. Lucas dos Santos Fernandez
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  2. Alexandre Molter
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  3. Fabio Silva Botelho
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Correspondence to Lucas dos Santos Fernandez.

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Fernandez, L.d.S., Molter, A. & Botelho, F.S. Simultaneous topology optimization and proportional actuators localization. SeMA 74, 385–409 (2017). https://doi.org/10.1007/s40324-016-0090-0

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  • DOI: https://doi.org/10.1007/s40324-016-0090-0

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