French version

Optimal design of structures

MAP 562

(G. Allaire)


Warning ! This web site is not updated anymore. All informations are now available on the Moodle web site featuring all courses at Ecole Polytechnique. The lecture notes of this course (in French) have been published by Springer in the series "Mathématiques et Applications", volume 58, 2007, 280 p., 91 illus., ISBN-10: 3-540-36710-1, ISBN-13: 978-3-540-36710-9.

Students following this course can borrow the textbook "Conception optimale des structures" at the library of Ecole Polytechnique. The course will be taught in English. The course will take place every Wednesday afternoon. During 4 hours there will be a mix of lectures, exercizes, numerical examples and personal projects. The students must bring their computer with the FreeFem++ software installed.

The web site for the numerical exercizes (and slides) is here.

The slides of each class can be downloaded below.

  • class of December 2nd, 2015
  • class of December 9th, 2015
  • class of January 7th, 2015
  • class of January 14th, 2015
  • class of January 21th, 2015
  • class of January 28th, 2015
  • class of February 4th, 2015
  • class of February 11th, 2015
  • class of February 18th, 2015 (lecture notes by Olivier Pantz)
  • The purpose of this course is to provide the basis of mathematical models and numerical algorithms for the optimal design of structures. Thanks to the enormous progress in mechanical modelling, numerical analysis and above all computer power in recent decades, it is nowadays relatively easy to design a structure (for example, a bridge, an aeroplane wing, a car body, etc.) by carrying out simulations and calculations on a computer. Nevertheless, during the design of a new structure one is frequently asked to try different possibilities and to modify them in order to improve them. This could turn out to be a very tedious task if it was done entirely by hand and if it relied solely on the designer's intuition. This is why it is necessary to develop automatic optimization methods for structures.

    This course focuses on the mathematical methods and numerical algorithms which are the keys to the automatic computerized process of shape optimization. It is not intended to develop the heuristic and mechanical intuitions used for a "trial and error" approach of optimal design.

    The reader may find many numerical examples (pictures, movies, programs), as well as many links on web sites dedicated to optimal design (including commercial softwares which are a testimony of its industrial impact), on the web page of the optimal design group at Ecole Polytechnique.

    For students who do not feel comfortable with English, here is a little glossary with French translations.

    Exams of the previous years

  • Sujet de l'examen (mars 2002)
  • Corrigé de l'examen (mars 2002)
  • Sujet de l'examen (mars 2003)
  • Corrigé de l'examen (mars 2003)
  • Sujet de l'examen (mars 2004)
  • Corrigé de l'examen (mars 2004)
  • Sujet de l'examen (mars 2005)
  • Corrigé de l'examen (mars 2005)
  • Sujet de l'examen (mars 2006)
  • Corrigé de l'examen (mars 2006)
  • Sujet de l'examen (mars 2007)
  • Corrigé de l'examen (mars 2007)
  • Sujet de l'examen (mars 2008)
  • Corrigé de l'examen (mars 2008)
  • Sujet de l'examen (mars 2009)
  • Corrigé de l'examen (mars 2009)
  • Sujet de l'examen (mars 2010)
  • Corrigé de l'examen (mars 2010)
  • Written exam (march 2011)
  • Solution of the exam (march 2011)
  • Written exam (march 2012)
  • Solution of the exam (march 2012)
  • Written exam (march 2013)
  • Solution of the exam (march 2013)
  • Written exam (march 2014)
  • Solution of the exam (march 2014)
  • Written exam (march 2015)
  • Solution of the exam (march 2015)
  • A few computer programs which are used to illustrate this course

    Try a shape optimization toolbox written for the Freefem++ software.

    Everything started with this historical paper of J. Hadamard (1908)

    Hadamard paper