An Introduction to the Topological Derivative Method

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.

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

Autor*in

Antonio André Novotny

Themen in »An Introduction to the Topological Derivative Method«

Topological derivatives Sensitivity analysis Asymptotic analysis Topology optimization Shape optimization Necessary optimality condition Nonconvex optimization partial differential equations

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