Mathematical Methods in Elasticity Imaging PDF Download

Author: Habib Ammari
Publisher: Princeton University Press
ISBN: 0691165319
Category : Mathematics
Languages : en
Pages : 240

View

Book Description
This book is the first to comprehensively explore 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.

Author: Philippe G. Ciarlet
Publisher: SIAM
ISBN: 1611976782
Category : Mathematics
Languages : en
Pages : 521

View

Book Description
The first book of a three-volume set, Three-Dimensional Elasticity covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. It includes the known existence theorems, either via the implicit function theorem or via the minimization of the energy (John Ball’s theory). An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

Author: Jerrold E. Marsden
Publisher: Courier Corporation
ISBN: 0486142272
Category : Technology & Engineering
Languages : en
Pages : 578

View

Book Description
Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.

Author:
Publisher: Elsevier
ISBN: 0080535917
Category : Mathematics
Languages : en
Pages : 561

View

Book Description
The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established.In the nonlinear case, again after ad hoc scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Kármán equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.

Author:
Publisher: Elsevier
ISBN: 0080875416
Category : Technology & Engineering
Languages : en
Pages : 495

View

Book Description
This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.

Author: Grace Qiao Zhang
Publisher: Bloomsbury Publishing
ISBN: 1350029602
Category : Language Arts & Disciplines
Languages : en
Pages : 217

View

Book Description
In Vague Language, Elasticity Theory and the Use of 'Some', Nguyet Nhu Le and Grace Qiao Zhang present the first comprehensive study of the word 'some', focusing on its elasticity. In particular, they consider how 'some' is both a quantifier and a qualifier, has positive or negative meanings, and has local and global interpretations. They show that the word is used across a meaning continuum and can be used to convey a range of states, including approximation, uncertainty, politeness, and evasion. Finally, they demonstrate that the functions of 'some' are also multi-directional and non-categorical, consisting of four major functions (right amount of information, mitigation, withholding information, and discourse management). Based on naturally-occurring classroom data of L1 (American English) and L2 (Chinese- and Vietnamese-speaking learners of English) speakers, Vague Language shows that L2 speakers used 'some' more than L1 speakers and explores the significance of this, particularly taking account of speakers' language ability and cultural backgrounds. While this book focuses on the single word 'some', the authors' discussion has important implications for language studies more generally, as they call for a rethinking of our approaches to language study and more attention to its elasticity.

Author: Stuart Antman
Publisher: Springer Science & Business Media
ISBN: 1475741472
Category : Mathematics
Languages : en
Pages : 762

View

Book Description
The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.

Author: Martin H. Sadd
Publisher: Elsevier
ISBN: 008047747X
Category : Technology & Engineering
Languages : en
Pages : 474

View

Book Description
Although there are several books in print dealing with elasticity, many focus on specialized topics such as mathematical foundations, anisotropic materials, two-dimensional problems, thermoelasticity, non-linear theory, etc. As such they are not appropriate candidates for a general textbook. This book provides a concise and organized presentation and development of general theory of elasticity. This text is an excellent book teaching guide. - Contains exercises for student engagement as well as the integration and use of MATLAB Software - Provides development of common solution methodologies and a systematic review of analytical solutions useful in applications of

Author: Hashimzade, Nigar
Publisher: Edward Elgar Publishing
ISBN: 1788976487
Category : Business & Economics
Languages : en
Pages : 672

View

Book Description
Written in a comprehensive yet accessible style, this Handbook introduces readers to a range of modern empirical methods with applications in microeconomics, illustrating how to use two of the most popular software packages, Stata and R, in microeconometric applications.

Author: Nigar Hashimzade
Publisher: Edward Elgar Publishing
ISBN: 0857931024
Category : Business & Economics
Languages : en
Pages : 627

View

Book Description
This comprehensive Handbook presents the current state of art in the theory and methodology of macroeconomic data analysis. It is intended as a reference for graduate students and researchers interested in exploring new methodologies, but can also be employed as a graduate text. The Handbook concentrates on the most important issues, models and techniques for research in macroeconomics, and highlights the core methodologies and their empirical application in an accessible manner. Each chapter is largely self-contained, whilst the comprehensive introduction provides an overview of the key statistical concepts and methods. All of the chapters include the essential references for each topic and provide a sound guide for further reading. Topics covered include unit roots, non-linearities and structural breaks, time aggregation, forecasting, the Kalman filter, generalised method of moments, maximum likelihood and Bayesian estimation, vector autoregressive, dynamic stochastic general equilibrium and dynamic panel models. Presenting the most important models and techniques for empirical research, this Handbook will appeal to students, researchers and academics working in empirical macro and econometrics.