Shape Optimization by the Homogenization Method

Gregoire Allaire

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English

Springer Verlag
01 June 2002

Mathematics & Sciences; Engineering: general; Maths for engineers; Structural engineering

Series: Applied Mathematical Sciences

This book provides an introduction to the theory and numerical developments of the homogenization method. Its main features are: a comprehensive presentation of homogenization theory; an introduction to the theory of two-phase composite materials;a detailed treatment of structural optimization by using homogenization; a complete discussion of the resulting numerical algorithms with many documented test problems. It will be of interest to researchers, engineers, and advanced graduate students in applied mathematics, mechanical engineering, and structural optimization.

By: Gregoire Allaire
Imprint: Springer Verlag
Country of Publication: United States
Dimensions: Height: 235mm, Width: 155mm, Spine: 26mm
Weight: 1.880kg
ISBN: 9780387952987
ISBN 10: 0387952985
Series: Applied Mathematical Sciences
Publication Date: 01 June 2002
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Reviews for Shape Optimization by the Homogenization Method

From the reviews: The book is a research monograph, but the structure and completeness of the presentation means that the book constitutes a good basis for a graduate course in applied mathematics. The rigorous mathematical presentation is supplemented with numerous remarks and comments which discuss the subject in broader terms, greatly simplifying the reading process. ... The book is a welcome and up-to-date addition to the literature in the area and it is necessary reading for any researcher and student ... (M.P. Bendsoe, Structural Multidisciplinary Optimization, 5, 2002) The book is very well structured, very clearly written, very well motivated, and complete in its treatment of modelling, analysis and simulation. It will be a basic reference for whoever wants to deeply understand homogenization from the point of view of its application to optimal design. The treatment is right to the point, a quality that is very much appreciated by readers. In summary, I believe this text may become a main source for the subject of optimal design and shape optimization. (Pablo Pedregal, Mathematical Reviews, 2002 h) The book under review presents a comprehensive introduction to the homogenisation method applied to optimal design, including many proofs which were hitherto only scattered throughout the literature ... this one provides the most complete treatment of numerical methods ... A number of realistic examples, mostly for elasticity, has been developed in detail. ... In summary, we would like to warmly recommend this book to anybody working in optimal shape design, composites and homogenisation, as well to those who wish to enter these fields. (Nenad Antonic and Marko Vrdoljak, Zentralblatt MATH, 990:15, 2002)