An Introduction to the Topological Derivat...

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Beschreibung

This book presents the topological derivative method through selected examples, using a direct approach based on calculus of variations combined with compound asymptotic analysis. This new concept in shape optimization has applications in many different fields such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena. In particular, the topological derivative is used here in numerical methods of shape optimization, with applications in the context of compliance structural topology optimization and topology design of compliant mechanisms. Some exercises are offered at the end of each chapter, helping the reader to better understand the involved concepts.

Über den Autor

Antonio André Novotny is a Senior Researcher at the National Laboratory for Scientific Computing, Petrópolis, Brazil. His research topics include the theoretical development and applications of the topological derivative method to shape and topology optimization; inverse problems; imaging processing; multi-scale material design; and mechanical modeling, including damage and fracture phenomena.

Jan Sokolowski is a Full Professor at the Institute of Mathematics (IECL) at the Université de Lorraine in Nancy, France, and at the Polish Academy of Sciences' Systems Research Institute. He has published five monographs with Springer and Birkhauser, and over 200 research papers in international journals. His research focuses on shape and topology optimization for the systems described by partial differential equations.

Zusammenfassung

Introduces the concept of topological derivative in a simple and pedagogical manner using a direct approach based on calculus of variations combined with compound asymptotic analysis

Offers numerical methods in shape optimization, including algorithms and applications in the context of compliance structural topology optimization and topology design of compliant mechanisms

Explores the mathematical aspects of topological asymptotic analysis as well as on applications of the topological derivative in computational mechanics, including shape and topology optimization

Inhaltsverzeichnis

Introduction.- Singular Domain Perturbation.- Regular Domain Perturbation.- Domain Truncation Method.- Topology Design Optimization.- Appendix: Tensor Calculus.- References.- Index.

Details

Erscheinungsjahr:	2020
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	124
Reihe:	SpringerBriefs in Mathematics
Inhalt:	x 114 S. 18 s/w Illustr. 6 farbige Illustr. 114 p. 24 illus. 6 illus. in color.
ISBN-13:	9783030369149
ISBN-10:	3030369145
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Soko¿owski, Jan Novotny, Antonio André
Auflage:	1st ed. 2020
Hersteller:	Springer International Publishing Springer International Publishing AG SpringerBriefs in Mathematics
Maße:	235 x 155 x 8 mm
Von/Mit:	Jan Soko¿owski (u. a.)
Erscheinungsdatum:	22.01.2020
Gewicht:	0,201 kg

preigu-id: 117669527