This book presents the topological derivative method through selected examples, using a direct approach based on the combination of calculus of variations combined and 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. The topological derivative is particularly useful in numerical methods of shape optimization, with applications in cases like 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.A valuable resource for researchers and graduate students in applied mathematics and computational mechanics, the book can also be used as lecture notes in graduate and advanced courses on the subject. weiterlesen