Nonlinear Theory Of Elastic Plates
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Nonlinear Theory Of Elasticity
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Author : Larry Alan Taber
language : en
Publisher: World Scientific
Release Date : 2004
Nonlinear Theory Of Elasticity written by Larry Alan Taber and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
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.
Nonlinear Theory Of Elastic Plates
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Author : Anh Le Van
language : en
Publisher: Elsevier
Release Date : 2017-05-31
Nonlinear Theory Of Elastic Plates written by Anh Le Van and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-31 with Mathematics categories.
Nonlinear Theory of Elastic Plates provides the theoretical materials necessary for the three plate models—Cosserat plates, Reissner-Mindlin plates and Kirchhoff-Love plates— in the context of finite elastic deformations. One separate chapter is devoted to the linearized theory of Kirchhoff-Love plates, which allows for the study of vibrations of a pre-stressed plate and the static buckling of a plate. All mathematical results in the tensor theory in curvilinear coordinates necessary to investigate the plate theory in finite deformations are provided, making this a self-contained resource. - Presents the tricky process of linearization, which is rarely dealt with, but explained in detail in a separate chapter - Organized in a mathematical style, with definitions, hypotheses, theorems and proofs clearly stated - Presents every theorem with its accompanying hypotheses, enabling the reader to quickly recognize the conditions of validity in results
Vibrations Of Elastic Plates
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Author : Yi-Yuan Yu
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-04-25
Vibrations Of Elastic Plates written by Yi-Yuan Yu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-04-25 with Science categories.
This book deals with the dynamical modeling of thin elastic structures, such as beams, plates and shells - particularly, the linear and nonlinear vibrations in these structures. The approach makes systematic use of variational equations of motion.
Nonlinear Mechanics Of Shells And Plates In Composite Soft And Biological Materials
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Author : Marco Amabili
language : en
Publisher: Cambridge University Press
Release Date : 2018-11
Nonlinear Mechanics Of Shells And Plates In Composite Soft And Biological Materials written by Marco Amabili and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11 with Mathematics categories.
This book guides the reader into the modelling of shell structures in applications where advanced composite materials or complex biological materials must be described with great accuracy. A valuable resource for researchers, professionals and graduate students, it presents a variety of practical concepts, diagrams and numerical results.
Poisson Theory Of Elastic Plates
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Author : Kaza Vijayakumar
language : en
Publisher: Springer Nature
Release Date : 2021-01-25
Poisson Theory Of Elastic Plates written by Kaza Vijayakumar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-25 with Technology & Engineering categories.
This groundbreaking book resolves the main lacuna in Kirchhoff theory of bending of plates in the Poisson-Kirchhoff boundary conditions paradox through the introduction of auxiliary problem governing transverse stresses. The book highlights new primary bending problem which is formulated and analyzed by the application of developed Poisson theory. Analysis with prescribed transverse stresses along faces of the plate, neglected in most reported theories, is presented with an additional term in displacements. The book presents a systematic procedure for the analysis of unsymmetrical laminates. This volume will be a useful reference for students, practicing engineers as well as researchers in applied mechanics.
An Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates
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Author : Raymond David Mindlin
language : en
Publisher: World Scientific
Release Date : 2006
An Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates written by Raymond David Mindlin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Technology & Engineering categories.
This book by the late R D Mindlin is destined to become a classic introduction to the mathematical aspects of two-dimensional theories of elastic plates. It systematically derives the two-dimensional theories of anisotropic elastic plates from the variational formulation of the three-dimensional theory of elasticity by power series expansions. The uniqueness of two-dimensional problems is also examined from the variational viewpoint. The accuracy of the two-dimensional equations is judged by comparing the dispersion relations of the waves that the two-dimensional theories can describe with prediction from the three-dimensional theory. Discussing mainly high-frequency dynamic problems, it is also useful in traditional applications in structural engineering as well as provides the theoretical foundation for acoustic wave devices.
Theory And Analysis Of Elastic Plates And Shells Second Edition
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Author : J. N. Reddy
language : en
Publisher: CRC Press
Release Date : 1999-02-10
Theory And Analysis Of Elastic Plates And Shells Second Edition written by J. N. Reddy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-10 with Technology & Engineering categories.
This text presents a complete treatment of the theory and analysis of elastic plates. It provides detailed coverage of classic and shear deformation plate theories and their solutions by analytical as well as numerical methods for bending, buckling and natural vibrations. Analytical solutions are based on the Navier and Levy solution method, and numerical solutions are based on the Rayleigh-Ritz methods and finite element method. The author address a range of topics, including basic equations of elasticity, virtual work and energy principles, cylindrical bending of plates, rectangular plates and an introduction to the finite element method with applications to plates.
Nonlinear Problems Of Elasticity
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Author : Stuart Antman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Nonlinear Problems Of Elasticity written by Stuart Antman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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.
Nonlinear Structural Mechanics
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Author : Walter Lacarbonara
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-09
Nonlinear Structural Mechanics written by Walter Lacarbonara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-09 with Science categories.
This book reviews the theoretical framework of nonlinear mechanics, covering computational methods, applications, parametric investigations of nonlinear phenomena and mechanical interpretation towards design. Builds skills via increasing levels of complexity.
Elasticity And Geometry
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Author : Basile Audoly
language : en
Publisher: Oxford University Press
Release Date : 2010-06-24
Elasticity And Geometry written by Basile Audoly and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.
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.