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Shape and Topology Optimization Group at CMAP
Welcome to the home page of the Shape and Topology Optimization Group of the Centre de Mathématiques Appliquées de l'École Polytechnique (CMAP). Its members are:
  • Grégoire Allaire
  • Aloïs Bissuel
  • Gabriel Delgado
  • Perle Geoffroy
  • Aymeric Maury
  • Georgios Michailidis
  • Dimitri Nicolas
  • Jean-Léopold Vié
  • Les collaborateurs extérieurs (anciens ou présents) de ce groupe sont :
  • Sylvie Aubry (Lawrence Livermore National Laboratory)
  • Jean-François Babadjian (Université Pierre et Marie Curie)
  • Zakaria Belhachmi (Université de haute Alsace)
  • Éric Bonnetier (Université Joseph Fourier)
  • Jonathan Chetboun (Dassault Aviation)
  • Charles Dapogny (Université Joseph Fourier)
  • Gilles Francfort (Université Paris-Nord)
  • Frédéric de Gournay (Université Paul Sabatier)
  • Sergio Gutiérrez (Pontifical Catholic University of Chile)
  • François Jouve (Université Paris Diderot)
  • Alex Kelly (Duke University)
  • Robert Kohn (New York University)
  • Hervé Maillot (Université d'Orléans)
  • Olivier Pantz (Université de Nice Sophia-Antipolis)
  • Marc Schoenauer (INRIA)
  • Anca-Maria Toader (Lisboa University)
  • Karim Trabelsi
  • Nicolas Van Goethem (Lisboa University)
  • Here is our list of publications.

    Other related web pages.

    Rodin project.

    A Scilab code for shape optimization by the level set method.

    A FreeFem++ toolbox for shape optimization.

    All the pictures and animations have been generated with xd3d.

    Structural optimization is a major concern in the design of mechanical systems in the industry (civil engineering, car makers, aeronautics, aerospace). Engineers do not content themselves with a mere improvement of a few mechanical properties, but they strive for a global optimization of weight, rigidity, resistence and cost.

    Traditionnaly, engineers proceed by trial and error, and optimization is really a matter of intuition and know-how. This is of course an old-fashion, costly, and imperfect way of optimizing. The modern trend is to use more and more numerical softwares which simultaneously analyze and optimize many possible designs, making optimal design an automatic process.

    We develop different algorithms to compute optimal shapes and structures. More details, as well as many numerical results, can be obtained by clicking on the links below.

    Compliance and Eigenvalues
Shape Optimization by the Homogenization Method
    Compliance and Eigenvalues
    Topology Optimization
    by the Homogenization Method
    Other objective functions. Mechanisms and MEMS
    Other objective functions.
    Mechanisms and MEMS
    Levelset Method
    Levelset method
    Shape sensitivity method
    Shape sensitivity