An Introduction to the Topological Derivative Method
1st Edition
Published on 22. January 2020
Book
Paperback/Softback
X, 114 pages
978-3-030-36914-9 (ISBN)
Description
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.
More details
Series
Edition
1st ed. 2020
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Primary & secondary/elementary & high school
Illustrations
18 s/w Abbildungen, 6 farbige Abbildungen
X, 114 p. 24 illus., 6 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 8 mm
Weight
201 gr
ISBN-13
978-3-030-36914-9 (9783030369149)
DOI
10.1007/978-3-030-36915-6
Schweitzer Classification
Other editions
Additional editions
Antonio André Novotny | Jan Sokolowski
An Introduction to the Topological Derivative Method
E-Book
01/2020
1st Edition
Springer
€64.19
Available for download
Persons
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.
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.
Content
Introduction.- Singular Domain Perturbation.- Regular Domain Perturbation.- Domain Truncation Method.- Topology Design Optimization.- Appendix: Tensor Calculus.- References.- Index.