Conception optimale de structures

"Conception optimale des structures" est une introduction à la conception optimale de structures, appelée aussi optimisation de formes. Il est principalement destiné à un public mixte de mathématiciens appliqués et de mécaniciens que relient un même intérêt pour les applications numériques. Il traite de tous les aspects de l'optimisation de formes, paramétrique, géométrique et topologique, et fait une large place aux algorithmes numériques, méthodes de gradient et méthodes stochastiques (avec une contribution originale de Marc Schoenauer pour ce dernier point). En particulier, la plupart des algorithmes d'optimisation de structures ont été implémentés dans le logiciel FreeFem++ d'éléments finis et les programmes sont disponibles librement sur le web.

"Conception optimale des structures" is devoted to structural or shape optimization and is intended for a mixed audience of applied mathematicians and mechanicians. It discusses parametric, geometric and topology optimization and gives deterministic and stochastic numerical algorithms (implemented in the FreeFem++ finite element software).

• algorithms
• analyse numérique
• calcul des structures
• finite element method
• homogénéisation
• optimisation de formes
• optimization

From the reviews:

"This is an introductory book about optimal design of structures, or shape optimization, as the domain is also called. It is mainly designed for applied mathematicians and mechanicians interested in numerics. It describes the three main approaches in shape optimization (parametrical, geometrical and topological) and presents numerical algorithms, gradient methods and stochastic methods … . A large number of references is provided at the end of each chapter." (Anca-Maria Toader, Mathematical Reviews, Issue 2008 c)

"This book corresponds to lectures given by the author at École Polytechnique, France. It gives a wide overview of problems and methods in shape optimization. … an excellent introduction in this field and it may concern a large audience going from engineers dealing with problems in structural mechanics to researchers interested by numerical calculations in shape optimization. … is nicely written and its reading is very pleasant. … no other text book in this field gives a so wide overview in less than 300 pages." (Jean-Pierre Raymond, Zentralblatt MATH, Vol. 1132 (10), 2008)

• Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128, France

  Grégoire Allaire

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