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Interaction of Mechanics and Mathematics

Topological Derivatives in Shape Optimization

Authors: Novotny, Antonio André, Sokołowski, Jan

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  • First monograph describing in details the new developments in shape optimization for elliptic boundary value problems
  • Presents a wide spectrum of examples and techniques for
  • learning how to use the modern mathematics in applied shape optimization of structures
  • Makes this important field of research accessible for the students of mathematics and of mechanics
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About this book

The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested on the mathematical aspects of topological asymptotic analysis as well as on applications of topological derivatives in computation mechanics.

Reviews

From the reviews:

“The main aim of the presented book is the presentation of topological derivatives for a wide class of elliptic problems with the applications in numerical methods of shape and topology optimization. This volume is primarily addressed to applied mathematicians working in the field of partial differential equations and their applications, especially those concerned with numerical aspects. However, the book will also be useful for applied scientists from engineering and physics.” (Jan Lovíšek, zbMATH, Vol. 1276, 2014)

“The book under review concerns new methods of solving a class of shape optimization problems appearing in continuum mechanics, mainly in solid mechanics, composites and plate-like bodies. … The theoretical results are illustrated by numerical examples. Moreover, carefully selected exercises are provided. This valuable book fills a gap in the literature on topology optimization.” (Tomasz Lewiński, Mathematical Reviews, August, 2013)

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $169.00
price for USA in USD
  • ISBN 978-3-642-35245-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $219.99
price for USA in USD
  • ISBN 978-3-642-35244-7
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Topological Derivatives in Shape Optimization
Authors
Series Title
Interaction of Mechanics and Mathematics
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-35245-4
DOI
10.1007/978-3-642-35245-4
Softcover ISBN
978-3-642-35244-7
Series ISSN
1860-6245
Edition Number
1
Number of Pages
XII, 324
Number of Illustrations
68 b/w illustrations
Topics

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