Nonlinear Theory Of Elastic Plates

Author : Anh Le Van
Publisher : Elsevier
Page : 212 pages
File Size : 42,6 Mb
Release : 2017-05-31
Category : Mathematics
ISBN : 9780081023594

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Nonlinear Theory of Elastic Plates by Anh Le Van Pdf

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

Author : Larry A Taber
Publisher : World Scientific
Page : 416 pages
File Size : 45,5 Mb
Release : 2004-02-19
Category : Science
ISBN : 9789814483391

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Nonlinear Theory Of Elasticity: Applications In Biomechanics by Larry A Taber Pdf

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 : Yi-Yuan Yu
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461223382

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Vibrations of Elastic Plates by Yi-Yuan Yu Pdf

This book is based on my experiences as a teacher and as a researcher for more than four decades. When I started teaching in the early 1950s, I became interested in the vibrations of plates and shells. Soon after I joined the Polytechnic Institute of Brooklyn as a professor, I began working busily on my research in vibrations of sandwich and layered plates and shells, and then teaching a graduate course on the same subject. Although I tried to put together my lecture notes into a book, I never finished it. Many years later, I came to the New Jersey Institute of Technology as the dean of engineering. When I went back to teaching and looked for some research areas to work on, I came upon laminated composites and piezoelectric layers, which appeared to be natural extensions of sandwiches. Working on these for the last several years has brought me a great deal of joy, since I still am able to find my work relevant. At least I can claim that I still am pursuing life-long learning as it is advocated by educators all over the country. This book is based on the research results I accumulated during these two periods of my work, the first on vibrations and dynamical model ing of sandwiches, and the second on laminated composites and piezoelec tric layers.

Author : A. Libai
Publisher : Elsevier
Page : 429 pages
File Size : 40,5 Mb
Release : 2012-12-02
Category : Technology & Engineering
ISBN : 9780323150811

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The Nonlinear Theory of Elastic Shells by A. Libai Pdf

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 : V. Panc
Publisher : Springer Science & Business Media
Page : 750 pages
File Size : 51,5 Mb
Release : 1975-04-30
Category : Science
ISBN : 902860104X

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Theories of elastic plates by V. Panc Pdf

The present monograph deals with refined theories of elastic plates in which both bending and transverse shear effects are taken into account and with some of their applications. Generally these more exact theories result in inte gration problems of the sixth order; consequently, three mutually independent boundary conditions at each edge of the plate are required. This is in perfect agreement with the conclusions of the theory of elasticity. The expressions for shearing forces following from refined theories are then valid for the whole investigated region including its boundary where the corresponding boundary conditions for these shearing forces can be prescribed. Quite different seems to be the situation in the classical Kirchhoff-Love's theory in which the influence of transverse shearing strains is neglected. Owing to this simplification the governing differential equation developed by the classical theory is of the fourth order only; consequently, the number of boundary conditions appurtenant to the applied mode of support appears now to be in disagreement with the order of the valid governing equation. Then, limiting the validity of the expressions for shearing forces to the open region of the middle plane and introducing the notion of the so called fictitious Kirchhoff's shearing forces for the boundary of the plate, three actual boundary conditions at each edge of the plate have to be replaced by two approximate conditions transformed in the Kirchhoff's sense.

Author : Clifford Truesdell
Publisher : Springer
Page : 755 pages
File Size : 43,7 Mb
Release : 2013-12-17
Category : Technology & Engineering
ISBN : 9783662397763

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Linear Theories of Elasticity and Thermoelasticity by Clifford Truesdell Pdf

Author : Marco Amabili
Publisher : Cambridge University Press
Page : 585 pages
File Size : 50,8 Mb
Release : 2018-11
Category : Science
ISBN : 9781107129221

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Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials by Marco Amabili Pdf

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.

Author : Raymond David Mindlin,Jiashi Yang
Publisher : World Scientific
Page : 211 pages
File Size : 54,9 Mb
Release : 2006
Category : Technology & Engineering
ISBN : 9789812703811

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An Introduction to the Mathematical Theory of Vibrations of Elastic Plates by Raymond David Mindlin,Jiashi Yang Pdf

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.

Author : J. N. Reddy
Publisher : CRC Press
Page : 561 pages
File Size : 41,6 Mb
Release : 2006-11-20
Category : Science
ISBN : 9780849384165

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Theory and Analysis of Elastic Plates and Shells by J. N. Reddy Pdf

Because plates and shells are common structural elements in aerospace, automotive, and civil engineering structures, engineers must understand the behavior of such structures through the study of theory and analysis. Compiling this information into a single volume, Theory and Analysis of Elastic Plates and Shells, Second Edition presents a complete

Author : Kaza Vijayakumar,Girish Kumar Ramaiah
Publisher : Springer Nature
Page : 149 pages
File Size : 45,9 Mb
Release : 2021-01-25
Category : Technology & Engineering
ISBN : 9789813342101

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Poisson Theory of Elastic Plates by Kaza Vijayakumar,Girish Kumar Ramaiah Pdf

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.

Author : V. V. Novozhilov
Publisher : Courier Corporation
Page : 260 pages
File Size : 42,7 Mb
Release : 1999-01-01
Category : Technology & Engineering
ISBN : 0486406849

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Foundations of the Nonlinear Theory of Elasticity by V. V. Novozhilov Pdf

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 : Anonim
Publisher : Elsevier
Page : 561 pages
File Size : 55,8 Mb
Release : 1997-07-22
Category : Mathematics
ISBN : 9780080535913

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Mathematical Elasticity by Anonim Pdf

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 : Iosif I. Vorovich
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 54,8 Mb
Release : 2008-01-08
Category : Technology & Engineering
ISBN : 9780387227764

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Nonlinear Theory of Shallow Shells by Iosif I. Vorovich Pdf

This book presents rigorous treatment of boundary value problems in nonlinear theory of shallow shells. The consideration of the problems is carried out using methods of nonlinear functional analysis.

Author : Aleksandr Nikolaevich Guzʹ,Guriĭ Nikolaevich Savin,I. A. Tsurpal
Publisher : Unknown
Page : 20 pages
File Size : 55,6 Mb
Release : 1966
Category : Elastic plates and shells
ISBN : UIUC:30112106608836

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Stress Concentration about Curvilinear Holes in Physically Nonlinear Elastic Plates by Aleksandr Nikolaevich Guzʹ,Guriĭ Nikolaevich Savin,I. A. Tsurpal Pdf

An approximate solution method of plane physical nonlinear problems of stress concentration about curvilinear holes in thin plates made of a material subject to a nonlinear law of elasticity is given. The solutions are represented in the form of expansions in the small parameter mu and epsilon. The determination of the stress function F for a physically nonlinear elastic plate with a hole reduces for each approximation to the integration of nonlinear differential equations. Stress concentration about an elliptic hole is considered in zero, first, and second approximation. The coefficient of stress concentration kappa is found on the contour of the hole, depending nonlinearly on the tensile forces Rho, the ellipticity of the hole, and parameter lambda characterizing the mechanical properties of the material. Tables represent the values of the coefficient of stress concentration for various values of the parameters Rho, lambda and epsilon.

Author : Muthukrishnan Sathyamoorthy
Publisher : CRC Press
Page : 548 pages
File Size : 55,6 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351359818

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Nonlinear Analysis of Structures (1997) by Muthukrishnan Sathyamoorthy Pdf

Nonlinear Analysis of Structures presents a complete evaluation of the nonlinear static and dynamic behavior of beams, rods, plates, trusses, frames, mechanisms, stiffened structures, sandwich plates, and shells. These elements are important components in a wide variety of structures and vehicles such as spacecraft and missiles, underwater vessels and structures, and modern housing. Today's engineers and designers must understand these elements and their behavior when they are subjected to various types of loads. Coverage includes the various types of nonlinearities, stress-strain relations and the development of nonlinear governing equations derived from nonlinear elastic theory. This complete guide includes both mathematical treatment and real-world applications, with a wealth of problems and examples to support the text. Special topics include a useful and informative chapter on nonlinear analysis of composite structures, and another on recent developments in symbolic computation. Designed for both self-study and classroom instruction, Nonlinear Analysis of Structures is also an authoritative reference for practicing engineers and scientists. One of the world's leaders in the study of nonlinear structural analysis, Professor Sathyamoorthy has made significant research contributions to the field of nonlinear mechanics for twenty-seven years. His foremost contribution to date has been the development of a unique transverse shear deformation theory for plates undergoing large amplitude vibrations and the examination of multiple mode solutions for plates. In addition to his notable research, Professor Sathyamoorthy has also developed and taught courses in the field at universities in India, Canada, and the United States.