Mathematical Methods in Elasticity Imaging

丛 书 名：Princeton series in applied mathematics

作     者：Habib Ammari Elie Bretin Josselin Garnier Hyeonbae Kang Hyundae Lee Abdul Wahab 

I S B N：(纸本) 9780691165318 

出 版 社：Princeton University Press 

出 版 年：2015年

页      数：vii, 230 pages :页

主 题 词：elasticity imaging asymptotic imaging elastic wave propagation stability resolution elastic inclusion crack elastic structure nanoparticle cellular structure elasticity imaging asymptotic imaging elastic wave propagation stability resolution elastic inclusion crack elastic structure nanoparticle cellular structure 

学科分类：02[经济学] 07[理学] 08[工学] 070104[理学-应用数学] 070103[理学-概率论与数理统计] 070101[理学-基础数学] 0820[工学-石油与天然气工程] 0202[经济学-应用经济学] 020208[经济学-统计学] 080203[工学-机械设计及理论] 0805[工学-材料科学与工程（可授工学、理学学位）] 080502[工学-材料学] 0802[工学-机械工程] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 080102[工学-固体力学] 0702[理学-物理学] 0801[工学-力学（可授工学、理学学位）] 

馆 藏 号：201271818...

摘      要：This book comprehensively explores elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.