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Theories Of Elastic Plates
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Book Synopsis Theories of elastic plates by : V. Panc
Download or read book Theories of elastic plates written by V. Panc and published by Springer Science & Business Media. This book was released on 1975-04-30 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elementary Theory of Elastic Plates by : L. G. Jaeger
Download or read book Elementary Theory of Elastic Plates written by L. G. Jaeger and published by Elsevier. This book was released on 2013-09-24 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Theory of Elastic Plates deals with plate theory, particularly on the elastic behavior of initially flat thin plates subjected to loads, producing deflexions. This book discusses rectangular plates and circular plates subjected to different types of load conditions. This text describes the bending moment and curvature of beams, and gives the formula of principal axes, where the location of a neutral axis that experiences zero stress and strain, can be found. This book also notes how calculations can show small or negligible deflexions. The text discusses Possion's ratio effect and the Mohr's circle relationship. This text analyzes the various loads acting on different parts of the rectangular plate using the Navier method; the Levy's method is taken up when considerations are on other forms of boundary support on the rectangular plate. This book then addresses the circular plate that experiences bending moments and curvatures when it is placed under radially symmetric loads. This text explains the equation that is applicable in a radially symmetric case. This book also addresses understanding approximations of energy in stability problems when there is bending and twisting as shown in a strut with a certain thickness, radial length of the arms, and length of the strut. Engineers, physicists, architects, and designers of industrial equipment subject to heavy loads will appreciate the information found in this book.
Book Synopsis Poisson Theory of Elastic Plates by : Kaza Vijayakumar
Download or read book Poisson Theory of Elastic Plates written by Kaza Vijayakumar and published by Springer Nature. This book was released on 2021-01-25 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to the Mathematical Theory of Vibrations of Elastic Plates by : Raymond David Mindlin
Download or read book An Introduction to the Mathematical Theory of Vibrations of Elastic Plates written by Raymond David Mindlin and published by World Scientific. This book was released on 2006 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Sample Chapter(s). Chapter 1: Elements of the Linear Theory of Elasticity (416 KB). Contents: Elements of the Linear Theory of Elasticity; Solutions of the Three-Dimensional Equations; Infinite Power Series of Two-Dimensional Equations; Zero-Order Approximation; First-Order Approximation; Intermediate Approximations. Readership: Researchers in mechanics, civil and mechanical engineering and applied mathematics.
Book Synopsis Elastic Plates by : Herbert Reismann
Download or read book Elastic Plates written by Herbert Reismann and published by Wiley-Interscience. This book was released on 1988-07-25 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very Good,No Highlights or Markup,all pages are intact.
Book Synopsis Mathematical Elasticity, Volume II by : Philippe G. Ciarlet
Download or read book Mathematical Elasticity, Volume II written by Philippe G. Ciarlet and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Elasticity set contains three self-contained volumes that together provide the only modern treatise on elasticity. They introduce contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells. Each volume contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. An extended preface and extensive bibliography have been added to each volume to highlight the progress that has been made since the original publication. The first book, Three-Dimensional Elasticity, covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. In volume two, Theory of Plates, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. The objective of Theory of Shells, the final volume, is to show how asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear shell theories: membrane, generalized membrane, and flexural. 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.
Book Synopsis Theory and Analysis of Elastic Plates and Shells, Second Edition by : J. N. Reddy
Download or read book Theory and Analysis of Elastic Plates and Shells, Second Edition written by J. N. Reddy and published by CRC Press. This book was released on 1999-02-10 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Vibrations of Elastic Plates by : Yi-Yuan Yu
Download or read book Vibrations of Elastic Plates written by Yi-Yuan Yu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory and Analysis of Elastic Plates and Shells by : J. N. Reddy
Download or read book Theory and Analysis of Elastic Plates and Shells written by J. N. Reddy and published by CRC Press. This book was released on 2006-11-20 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Theories of elastic plates by : V. Panc
Download or read book Theories of elastic plates written by V. Panc and published by Springer. This book was released on 2014-01-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to the Mathematical Theory of Vibrations of Elastic Plates by : Raymond David Mindlin
Download or read book An Introduction to the Mathematical Theory of Vibrations of Elastic Plates written by Raymond David Mindlin and published by World Scientific. This book was released on 2006 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Simplified Analytical Methods of Elastic Plates by : Hideo Takabatake
Download or read book Simplified Analytical Methods of Elastic Plates written by Hideo Takabatake and published by Springer. This book was released on 2018-11-02 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents simplified analytical methodologies for static and dynamic problems concerning various elastic thin plates in the bending state and the potential effects of dead loads on static and dynamic behaviors. The plates considered vary in terms of the plane (e.g. rectangular or circular plane), stiffness of bending, transverse shear and mass. The representative examples include void slabs, plates stiffened with beams, stepped thickness plates, cellular plates and floating plates, in addition to normal plates. The closed-form approximate solutions are presented in connection with a groundbreaking methodology that can easily accommodate discontinuous variations in stiffness and mass with continuous function as for a distribution. The closed-form solutions can be used to determine the size of structural members in the preliminary design stages, and to predict potential problems with building slabs intended for human beings’ practical use.
Book Synopsis Anisotropic Elastic Plates by : Chyanbin Hwu
Download or read book Anisotropic Elastic Plates written by Chyanbin Hwu and published by Springer Science & Business Media. This book was released on 2010-08-09 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt: As structural elements, anisotropic elastic plates find wide applications in modern technology. The plates here are considered to be subjected to not only inplane load but also transverse load. In other words, both plane and plate bending problems as well as the stretching-bending coupling problems are all explained in this book. In addition to the introduction of the theory of anisotropic elasticity, several important subjects have are discussed in this book such as interfaces, cracks, holes, inclusions, contact problems, piezoelectric materials, thermoelastic problems and boundary element analysis.
Book Synopsis Theories and Applications of Plate Analysis by : Rudolph Szilard
Download or read book Theories and Applications of Plate Analysis written by Rudolph Szilard and published by John Wiley & Sons. This book was released on 2004-01-02 with total page 1062 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book by a renowned structural engineer offers comprehensive coverage of both static and dynamic analysis of plate behavior, including classical, numerical, and engineering solutions. It contains more than 100 worked examples showing step by step how the various types of analysis are performed.
Book Synopsis Theories of Plates and Shells by : Reinhold Kienzler
Download or read book Theories of Plates and Shells written by Reinhold Kienzler and published by Springer Science & Business Media. This book was released on 2013-06-01 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plate and shell theories experienced a renaissance in recent years. The potentials of smart materials, the challenges of adaptive structures, the demands of thin-film technologies and more on the one hand and the availability of newly developed mathematical tools, the tremendous increase in computer facilities and the improvement of commercial software packages on the other caused a reanimation of the scientific interest. In the present book the contributions of the participants of the EUROMECH Colloquium 444 "Critical Review of the Theories of Plates and Shells and New Applications" have been collected. The aim was to discuss the common roots of different plate and shell approaches, to review the current state of the art, and to develop future lines of research. Contributions were written by scientists with civil and mechanical engineering as well as mathematical and physical background.
Book Synopsis The Bending and Stretching of Plates by : E. H. Mansfield
Download or read book The Bending and Stretching of Plates written by E. H. Mansfield and published by Elsevier. This book was released on 2014-05-12 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bending and Stretching of Plates deals with elastic plate theory, particularly on small- and large-deflexion theory. Small-deflexion theory concerns derivation of basic equations, rectangular plates, plates of various shapes, plates whose boundaries are amenable to conformal transformation, plates with variable rigidity, and approximate methods. Large-deflexion theory includes general equations and some exact solutions, approximate methods in large-deflexion theory, asymptotic large-deflexion theories for very thin plates. Asymptotic theories covers membrane theory, tension field theory, and inextensional theory. The book explains stress-strain relations, effect of forces in the plane of the plate, and rectangular plates that have all edges simply supported, or where plates that have all edges clamped. The text also considers plates of constant thickness whose boundaries are circular, sector-shaped, elliptical, or triangular. Muskhelishvili (1933) addresses boundary value problems of plane stress using analytical methods of the biharmonic equation. The book also investigates some approximate methods of analysis of large-deflexion behavior of plates of constant thickness where there is either a uniformly distributed load, or a compressive load in the plane of the plate in excess of that necessary to cause initial buckling. The book explains that the engineer can use the principle of minimum potential energy to investigate large deflexion of plates. The text is suitable for structural engineers in civil, mechanical or marine engineering, as well as to structural research workers and students.
Book Synopsis Modern Trends in Structural and Solid Mechanics 2 by : Noel Challamel
Download or read book Modern Trends in Structural and Solid Mechanics 2 written by Noel Challamel and published by John Wiley & Sons. This book was released on 2021-06-08 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprised of three separate volumes presents the recent developments and research discoveries in structural and solid mechanics; it is dedicated to Professor Isaac Elishakoff. This second volume is devoted to the vibrations of solid and structural members. Modern Trends in Structural and Solid Mechanics 2 has broad scope, covering topics such as: exact and approximate vibration solutions of rods, beams, membranes, plates and three-dimensional elasticity problems, Bolotins dynamic edge effect, the principles of plate theories in dynamics, nano- and microbeams, nonlinear dynamics of shear extensible beams, the vibration and aeroelastic stability behavior of cellular beams, the dynamic response of elastoplastic softening oscillators, the complex dynamics of hysteretic oscillators, bridging waves, and the three-dimensional propagation of waves. This book is intended for graduate students and researchers in the field of theoretical and applied mechanics.
