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Introduction to the Topological Derivative Method 1st ed. 2020 [Minkštas viršelis]

  • Formatas: Paperback / softback, 114 pages, aukštis x plotis: 235x155 mm, weight: 203 g, 4 Tables, color; 6 Illustrations, color; 18 Illustrations, black and white; X, 114 p. 24 illus., 6 illus. in color., 1 Paperback / softback
  • Serija: SpringerBriefs in Mathematics
  • Išleidimo metai: 22-Jan-2020
  • Leidėjas: Springer Nature Switzerland AG
  • ISBN-10: 3030369145
  • ISBN-13: 9783030369149
  • Formatas: Paperback / softback, 114 pages, aukštis x plotis: 235x155 mm, weight: 203 g, 4 Tables, color; 6 Illustrations, color; 18 Illustrations, black and white; X, 114 p. 24 illus., 6 illus. in color., 1 Paperback / softback
  • Serija: SpringerBriefs in Mathematics
  • Išleidimo metai: 22-Jan-2020
  • Leidėjas: Springer Nature Switzerland AG
  • ISBN-10: 3030369145
  • ISBN-13: 9783030369149
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.
Introduction.- Singular Domain Perturbation.- Regular Domain Perturbation.- Domain Truncation Method.- Topology Design Optimization.- Appendix: Tensor Calculus.- References.- Index.
Antonio Andre Novotny is a Senior Researcher at the National Laboratory for Scientific Computing, Petropolis, 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 Universite 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.