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Truss optimization with multiple frequency constraints and automatic member grouping

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Abstract

This paper deals with sizing and shape structural optimization problems with respect to the minimization of the masses of truss structures considering multiple natural frequencies as the constraints of the problems. The sizing and shape design variables are discrete and continuous, respectively. It can be attractive to use a reduced number of distinct cross-sectional areas minimizing costs of fabrication, transportation, storing, checking, welding, and so on. Also, it is expected a labor-saving when the structure is welded, checked and so on. On the other hand, one can observe that the task of discovering the optimum member grouping is not trivial and leads to an exhaustive trial-and-error process. Cardinality constraints are adopted in order to obtain an automatic variable linking searching for the best member grouping of the bars of the trusses analyzed in this paper. A CRPSO (Craziness based Particle Swarm Optimization) is the search algorithm adopted in this paper. This algorithm uses a modified velocity expression and an operator called “craziness velocity” in order to avoid premature convergence. An Adaptive Penalty Method is adopted to handle the constraints. Six truss structures are analyzed, presenting very interesting results providing curves of tradeoff between the optimized weights versus the number of distinct cross-sectional areas used in these solutions.

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Acknowledgments

The authors wish to thank the referees that helped the quality of the paper, CNPq (305175/2013-0 e 305099/2014-0), FAPEMIG (TEC PPM 528/11, TEC PPM 388/14 and TEC APQ 00103-12) and CAPES for their support.

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Authors and Affiliations

  1. Department of Applied and Computational Mechanics, Faculty of Engineering, Federal University of Juiz de Fora, Juiz de Fora, Brazil

    José P. G. Carvalho, Afonso C. C. Lemonge & Patrícia H. Hallak

  2. Postgraduate Program in Computational Modeling, Federal University of Juiz de Fora, Juiz de Fora, Brazil

    Érica C. R. Carvalho

  3. Department of Computer Science, Institute of Exact Sciences, Federal University of Juiz de Fora, Juiz de Fora, Brazil

    Heder S. Bernardino

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  1. José P. G. Carvalho
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  2. Afonso C. C. Lemonge
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  3. Érica C. R. Carvalho
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  4. Patrícia H. Hallak
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  5. Heder S. Bernardino
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Correspondence to Afonso C. C. Lemonge.

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Carvalho, J.P.G., Lemonge, A.C.C., Carvalho, É.C.R. et al. Truss optimization with multiple frequency constraints and automatic member grouping. Struct Multidisc Optim 57, 547–577 (2018). https://doi.org/10.1007/s00158-017-1761-x

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