Metallic Foam Density Distribution Optimization Using Genetic Algorithms and Voronoi Tessellation

  • Pablo C. ResendeEmail author
  • Renato V. Linn
  • Branca F. de Oliveira
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 49)


Metallic foams have a very particular structure due to their high specific stiffness. Density plays an important role on their structural response and is also determinant to the foam’s weight. The main goal of this paper is to find an ideal density distribution to open-cell metallic foams in order to achieve optimized structural performance. A density distribution optimization using an irregular description of the foam by a Voronoi tessellation and a genetic algorithm for the numerical optimization is presented in this work. The structural analysis is performed with linear elastic beam finite elements and the foam structure is modeled as a Voronoi tessellation. The density is related to the number of Voronoi seeds, which may configure lighter or denser foams and vary throughout the model. The minimization and maximization of stiffness were analyzed for different structural applications in order to demonstrate the capability of the developed methodology.


Metallic foam Density optimization Voronoi tessellation Genetic algorithm 



We thank CNPq, CAPES, FAPERGS, CESUP, and PROPESQ/UFRGS for continuous support of our research projects.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Pablo C. Resende
    • 1
    Email author
  • Renato V. Linn
    • 2
  • Branca F. de Oliveira
    • 1
  1. 1.Graduate Program in Design (PGDesign)Federal University of Rio Grande do Sul (UFRGS)Porto AlegreBrazil
  2. 2.Graduate Program in Civil Engineering (PPGEC)Federal University of Rio Grande do Sul (UFRGS)Porto AlegreBrazil

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