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Author : Y. B. Fu,R. W. Ogden
Publisher : Cambridge University Press
Page : 541 pages
File Size : 40,7 Mb
Release : 2001-05-07
Category : Mathematics
ISBN : 9780521796958
Comprehensive introduction to nonlinear elasticity for graduates and researchers, covering new developments in the field.
Author : Larry A Taber
Publisher : World Scientific
Page : 416 pages
File Size : 43,7 Mb
Release : 2004-02-19
Category : Science
ISBN : 9789814483391
Soft biological tissues often undergo large (nearly) elastic deformations that can be analyzed using the nonlinear theory of elasticity. Because of the varied approaches to nonlinear elasticity in the literature, some aspects of the subject may be difficult to appreciate. This book attempts to clarify and unify those treatments, illustrating the advantages and disadvantages of each through various examples in the mechanics of soft tissues. Applications include muscle, arteries, the heart, and embryonic tissues.
Author : L.W. Ratner
Publisher : Elsevier
Page : 281 pages
File Size : 50,9 Mb
Release : 2003-11-12
Category : Science
ISBN : 9780080537603
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it can be done only with a destructive test for each structure. For building and explaining the theory, a new logical structure was introduced as the basis of the theory. One of the important physical implications of this logic is that it describes mathematically the universal domain of the possible stable physical relations.
Author : A.I. Lurie
Publisher : Elsevier
Page : 632 pages
File Size : 52,6 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780444597236
This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.
Author : V. V. Novozhilov
Publisher : Courier Corporation
Page : 260 pages
File Size : 51,5 Mb
Release : 1999-01-01
Category : Technology & Engineering
ISBN : 0486406849
This is an essential book for students and academicians alike. In addition to discussing theory, topics include the connection between stresses and strains in an isotropic elastic body, the geometry of strain, and much more. Deductions are explained in the simplest, most intuitive manner for wide accessibility. 1953 edition.
Author : Stuart Antman
Publisher : Springer Science & Business Media
Page : 762 pages
File Size : 49,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475741476
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 : R. W. Ogden
Publisher : Courier Corporation
Page : 544 pages
File Size : 40,9 Mb
Release : 2013-04-26
Category : Technology & Engineering
ISBN : 9780486318714
Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.
Author : A. Libai
Publisher : Elsevier
Page : 429 pages
File Size : 48,8 Mb
Release : 2012-12-02
Category : Technology & Engineering
ISBN : 9780323150811
The Nonlinear Theory of Elastic Shells: One Spatial Dimension presents the foundation for the nonlinear theory of thermoelastic shells undergoing large strains and large rotations. This book discusses several relatively simple equations for practical application. Organized into six chapters, this book starts with an overview of the description of nonlinear elastic shell. This text then discusses the foundation of three-dimensional continuum mechanics that are relevant to the shell theory approach. Other chapters cover several topics, including birods, beamshells, and axishells that begins with a derivation of the equations of motion by a descent from the equations of balance of linear and rotational momentum of a three-dimensional material continuum. This book discusses as well the approach to deriving complete field equations for one- or two-dimensional continua from the integral equations of motion and thermodynamics of a three-dimensional continuum. The final chapter deals with the analysis of unishells. This book is a valuable resource for physicists, mathematicians, and scientists.
Author : Arabinda Roy,Rasajit Kumar Bera
Publisher : CRC Press
Page : 597 pages
File Size : 54,8 Mb
Release : 2019-12-06
Category : Technology & Engineering
ISBN : 9781000758146
Linear and Non-Linear Deformations of Elastic Solids aims to compile the advances in the field of linear and non-linear elasticity through discussion of advanced topics. Broadly classified into two parts, it includes crack, contact, scattering and wave propagation in linear elastic solids and bending vibration, stability in non-linear elastic solids supported by MATLAB examples. This book is aimed at graduate students and researchers in applied mathematics, solid mechanics, applied mechanics, structural mechanics and includes comprehensive discussion of related analytical/numerical methods.
Author : Clifford Truesdell
Publisher : Springer
Page : 755 pages
File Size : 48,5 Mb
Release : 2013-12-17
Category : Technology & Engineering
ISBN : 9783662397763
Author : V. V. Novožilov
Publisher : Unknown
Page : 233 pages
File Size : 47,6 Mb
Release : 1953
Category : Electronic
ISBN : OCLC:638085727
Author : Martin H. Sadd
Publisher : Elsevier
Page : 474 pages
File Size : 50,5 Mb
Release : 2010-08-04
Category : Technology & Engineering
ISBN : 9780080477473
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 : Koichi Hashiguchi
Publisher : Elsevier
Page : 420 pages
File Size : 49,7 Mb
Release : 2020-06-19
Category : Technology & Engineering
ISBN : 9780128194294
Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity empowers readers to fully understand the constitutive equation of finite strain, an essential piece in assessing the deformation/strength of materials and safety of structures. The book starts by providing a foundational overview of continuum mechanics, elasticity and plasticity, then segues into more sophisticated topics such as multiplicative decomposition of deformation gradient tensor with the isoclinic concept and the underlying subloading surface concept. The subloading surface concept insists that the plastic strain rate is not induced suddenly at the moment when the stress reaches the yield surface but it develops continuously as the stress approaches the yield surface, which is crucially important for the precise description of cyclic loading behavior. Then, the exact formulations of the elastoplastic and viscoplastic constitutive equations based on the multiplicative decomposition are expounded in great detail. The book concludes with examples of these concepts and modeling techniques being deployed in real-world applications. Table of Contents: 1. Mathematical Basics 2. General (Curvilinear) Coordinate System 3. Description of Deformation/Rotation in Convected Coordinate System 4. Deformation/Rotation (Rate) Tensors 5. Conservation Laws and Stress Tensors 6. Hyperelastic Equations 7. Development of Elastoplastic Constitutive Equations 8. Multiplicative Decomposition of Deformation Gradient Tensor 9. Multiplicative Hyperelastic-based Plastic and Viscoplastic Constitutive Equations 10. Friction Model: Finite Sliding Theory Covers both the fundamentals of continuum mechanics and elastoplasticity while also introducing readers to more advanced topics such as the subloading surface model and the multiplicative decomposition among others Approaches finite elastoplasticity and viscoplasticty theory based on multiplicative decomposition and the subloading surface model Provides a thorough introduction to the general tensor formulation details for the embedded curvilinear coordinate system and the multiplicative decomposition of the deformation gradient
Author : Basile Audoly,Yves Pomeau
Publisher : Oxford University Press
Page : 597 pages
File Size : 47,7 Mb
Release : 2010-06-24
Category : Mathematics
ISBN : 9780198506256
We experience elasticity everywhere in everyday life. This book covers several modern aspects of the established field of elasticity theory, applying general methods of classical analysis including advanced nonlinear aspects to derive detailed solutions to specific problems. It can serve as an introduction to nonlinear methods in science.
Author : Valentin Valentinovič Novožilov
Publisher : Unknown
Page : 233 pages
File Size : 55,7 Mb
Release : 1953
Category : Electronic
ISBN : OCLC:488755329