An Introduction to the Topological Derivative Method (Springerbriefs in Mathematics)

Novotny, Antonio André/ Sokołowski, Jan

Springer Nature Switzerland AG（2020/01発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 114 p.
• 言語 ENG
• 商品コード 9783030369149
• DDC分類 515

Full 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.

Contents

Introduction.- Singular Domain Perturbation.- Regular Domain Perturbation.- Domain Truncation Method.- Topology Design Optimization.- Appendix: Tensor Calculus.- References.- Index.