The homogenization method for topology and shape optimization. Single and multiple loads case

Authors

  • Gregoire Allaire Commissariat a l'Energie Atomique, DRN/DMTISERMA, CEA Saclay, 91191 Gif sur Yvette et Laboratoire d'Analyse Numerique, Universite Paris 6
  • Zakaria Belhachmi Departement de Mathematiques, Universite de Metz, lle du Saulcy, 57045 Metz
  • Fran~ois Jouve Centre de Mathematiques Appliquees, URA.-CNRS 756, Ecole Polytechnique, 91128 Palaiseau

Keywords:

optimal design, homogenization, shape optimization, topology optimization, sequential laminates

Abstract

This paper is devoted to an elementary introduction to the homogenization methods applied to topology and shape optimization of elastic structures under single and multiple external loads. The single load case, in the context of minimum compliance and weight design of elastic structures, has been fully described in its theoretical as well as its numerical aspects in [4]. It is here briefly recalled. In the more realistic context of "multiple loads", i.e. when the structure is optimized with respect to more than one set of external forces, most of the obtained theoretical results remain true. However, the parameters that define optimal composite materials cannot be computed explicity. In this paper, a method to treat numerically the multiple loads case is proposed.

 

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Published

1996-06-24

How to Cite

Allaire, G. ., Belhachmi, Z. ., & Jouve, F. . (1996). The homogenization method for topology and shape optimization. Single and multiple loads case. European Journal of Computational Mechanics, 5(5-6), 649–672. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/3491

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Original Article