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Nonlinear Problems Of Elasticity
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Book Synopsis Nonlinear Problems of Elasticity by : Stuart Antman
Download or read book Nonlinear Problems of Elasticity written by Stuart Antman and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Theory of Elasticity by : Larry Alan Taber
Download or read book Nonlinear Theory of Elasticity written by Larry Alan Taber and published by World Scientific. This book was released on 2004 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Non-Linear Elastic Deformations by : R. W. Ogden
Download or read book Non-Linear Elastic Deformations written by R. W. Ogden and published by Courier Corporation. This book was released on 2013-04-26 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Contact Problems in Elasticity by : N. Kikuchi
Download or read book Contact Problems in Elasticity written by N. Kikuchi and published by SIAM. This book was released on 1988-01-01 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples.
Book Synopsis Nonlinear Elasticity; Proceedings by : Ronald Wayne Dickey
Download or read book Nonlinear Elasticity; Proceedings written by Ronald Wayne Dickey and published by . This book was released on 1973 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-Linear Theory of Elasticity by : A.I. Lurie
Download or read book Non-Linear Theory of Elasticity written by A.I. Lurie and published by Elsevier. This book was released on 2012-12-02 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Non-Linear Theory of Elasticity and Optimal Design by : L.W. Ratner
Download or read book Non-Linear Theory of Elasticity and Optimal Design written by L.W. Ratner and published by Elsevier. This book was released on 2003-11-12 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Linear and Non-Linear Deformations of Elastic Solids by : Arabinda Roy
Download or read book Linear and Non-Linear Deformations of Elastic Solids written by Arabinda Roy and published by CRC Press. This book was released on 2019-12-06 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Variational Methods in Nonlinear Elasticity by : Pablo Pedregal
Download or read book Variational Methods in Nonlinear Elasticity written by Pablo Pedregal and published by SIAM. This book was released on 2000-01-01 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the main vector variational methods developed to solve nonlinear elasticity problems. Presenting a general framework with a tight focus, the author provides a comprehensive exposition of a technically difficult, yet rapidly developing area of modern applied mathematics. The book includes the classical existence theory as well as a brief incursion into problems where nonexistence is fundamental. It also provides self-contained, concise accounts of quasi convexity, polyconvexity, and rank-one convexity, which are used in nonlinear elasticity.
Book Synopsis Linear Theories of Elasticity and Thermoelasticity by : Clifford Truesdell
Download or read book Linear Theories of Elasticity and Thermoelasticity written by Clifford Truesdell and published by Springer. This book was released on 2013-12-17 with total page 755 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Elasticity written by Y. B. Fu and published by Cambridge University Press. This book was released on 2001-05-07 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive introduction to nonlinear elasticity for graduates and researchers, covering new developments in the field.
Book Synopsis Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies by : Leonid M. Zubov
Download or read book Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies written by Leonid M. Zubov and published by Springer Science & Business Media. This book was released on 2008-09-11 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author applies methods of nonlinear elasticity to investigate the defects in the crystal structure of solids such as dislocations and disclinations that characterize the plastic and strength properties of many materials. Contrary to the geometrically motivated nonlinear theory of dislocations continuously distributed over the body, nonlinear analysis of isolated dislocations and disclinations is less developed; it is given for the first time in this book, and in a form accessible to both students and researchers. The general theory of Volterra's dislocations in elastic media under large deformations is developed. A number of exact solutions are found. The nonlinear approach to investigating the isolated defects produces results that often differ qualitatively from those of the linear theory.
Book Synopsis Mathematical Foundations of Elasticity by : Jerrold E. Marsden
Download or read book Mathematical Foundations of Elasticity written by Jerrold E. Marsden and published by Courier Corporation. This book was released on 2012-10-25 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Foundations of the Nonlinear Theory of Elasticity by : V. V. Novozhilov
Download or read book Foundations of the Nonlinear Theory of Elasticity written by V. V. Novozhilov and published by Courier Corporation. This book was released on 1999-01-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elasticity and Geometry by : Basile Audoly
Download or read book Elasticity and Geometry written by Basile Audoly and published by Oxford University Press. This book was released on 2010-06-24 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Three-Dimensional Elasticity written by and published by Elsevier. This book was released on 1988-04-01 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Linearized Theory of Elasticity by : William S. Slaughter
Download or read book The Linearized Theory of Elasticity written by William S. Slaughter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is derived from notes used in teaching a first-year graduate-level course in elasticity in the Department of Mechanical Engineering at the University of Pittsburgh. This is a modern treatment of the linearized theory of elasticity, which is presented as a specialization of the general theory of continuum mechanics. It includes a comprehensive introduction to tensor analysis, a rigorous development of the governing field equations with an emphasis on recognizing the assumptions and approximations in herent in the linearized theory, specification of boundary conditions, and a survey of solution methods for important classes of problems. Two- and three-dimensional problems, torsion of noncircular cylinders, variational methods, and complex variable methods are covered. This book is intended as the text for a first-year graduate course in me chanical or civil engineering. Sufficient depth is provided such that the text can be used without a prerequisite course in continuum mechanics, and the material is presented in such a way as to prepare students for subsequent courses in nonlinear elasticity, inelasticity, and fracture mechanics. Alter natively, for a course that is preceded by a course in continuum mechanics, there is enough additional content for a full semester of linearized elasticity.
