An Introduction to the Topological Derivative Method

Antonio André Novotny · Jan Sokołowski

Jan 2020 · Springer Nature

About this ebook

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.

About the author

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.