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Variational And Potential Methods In The Theory Of Bending Of Plates With Transverse Shear Deformation
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Book Synopsis Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation by : I. Chudinovich
Download or read book Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation written by I. Chudinovich and published by CRC Press. This book was released on 2000-06-13 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elastic plates form a class of very important mechanical structures that appear in a wide range of practical applications, from building bodies to microchip production. As the sophistication of industrial designs has increased, so has the demand for greater accuracy in analysis. This in turn has led modelers away from Kirchoff's classical theory fo
Book Synopsis Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation by : I. Chudinovich
Download or read book Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation written by I. Chudinovich and published by CRC Press. This book was released on 2000-06-13 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elastic plates form a class of very important mechanical structures that appear in a wide range of practical applications, from building bodies to microchip production. As the sophistication of industrial designs has increased, so has the demand for greater accuracy in analysis. This in turn has led modelers away from Kirchoff's classical theory for thin plates and toward increasingly refined models that yield not only the deflection of the middle section, but also account for transverse shear deformation. The improved performance of these models is achieved, however, at the expense of a much more complicated system of governing equations and boundary conditions. In this Monograph, the authors conduct a rigorous mathematical study of a number of boundary value problems for the system of partial differential equations that describe the equilibrium bending of an elastic plate with transverse shear deformation. Specifically, the authors explore the existence, uniqueness, and continuous dependence of the solution on the data. In each case, they give the variational formulation of the problems and discuss their solvability in Sobolev spaces. They then seek the solution in the form of plate potentials and reduce the problems to integral equations on the contour of the domain. This treatment covers an extensive range of problems and presents the variational method and the boundary integral equation method applied side-by-side. Readers will find that this feature of the book, along with its clear exposition, will lead to a firm and useful understanding of both the model and the methods.
Book Synopsis Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes by : Igor Chudinovich
Download or read book Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes written by Igor Chudinovich and published by Springer Science & Business Media. This book was released on 2005-11-27 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational and boundary integral equation techniques are two of the most useful methods for solving time-dependent problems described by systems of equations of the form 2 ? u = Au, 2 ?t 2 where u = u(x,t) is a vector-valued function, x is a point in a domain inR or 3 R,and A is a linear elliptic di?erential operator. To facilitate a better und- standing of these two types of methods, below we propose to illustrate their mechanisms in action on a speci?c mathematical model rather than in a more impersonal abstract setting. For this purpose, we have chosen the hyperbolic system of partial di?erential equations governing the nonstationary bending of elastic plates with transverse shear deformation. The reason for our choice is twofold. On the one hand, in a certain sense this is a “hybrid” system, c- sistingofthreeequationsforthreeunknownfunctionsinonlytwoindependent variables, which makes it more unusual—and thereby more interesting to the analyst—than other systems arising in solid mechanics. On the other hand, this particular plate model has received very little attention compared to the so-called classical one, based on Kirchho?’s simplifying hypotheses, although, as acknowledged by practitioners, it represents a substantial re?nement of the latter and therefore needs a rigorous discussion of the existence, uniqueness, and continuous dependence of its solution on the data before any construction of numerical approximation algorithms can be contemplated.
Book Synopsis Theories and Analyses of Beams and Axisymmetric Circular Plates by : J N Reddy
Download or read book Theories and Analyses of Beams and Axisymmetric Circular Plates written by J N Reddy and published by CRC Press. This book was released on 2022-06-30 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive textbook compiles cutting-edge research on beams and circular plates, covering theories, analytical solutions, and numerical solutions of interest to students, researchers, and engineers working in industry. Detailing both classical and shear deformation theories, the book provides a complete study of beam and plate theories, their analytical (exact) solutions, variational solutions, and numerical solutions using the finite element method. Beams and plates are some of the most common structural elements used in many engineering structures. The book details both classical and advanced (i.e., shear deformation) theories, scaling in complexity to aid the reader in self-study, or to correspond with a taught course. It covers topics including equations of elasticity, equations of motion of the classical and first-order shear deformation theories, and analytical solutions for bending, buckling, and natural vibration. Additionally, it details static as well as transient response based on exact, the Navier, and variational solution approaches for beams and axisymmetric circular plates, and has dedicated chapters on linear and nonlinear finite element analysis of beams and circular plates. Theories and Analyses of Beams and Axisymmetric Circular Plates will be of interest to aerospace, civil, materials, and mechanical engineers, alongside students and researchers in solid and structural mechanics.
Download or read book Analysis of Plates written by T.K Varadan and published by ALPHA SCIENCE INTERNATIONAL LIMITED. This book was released on 1999-01-01 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the classical plate theory most commonly used for the analysis of thin metallic plate structures. The basic assumptions of the plate theory are not straightaway taken for granted, but are deduced as logical inferences from a three-dimensional elasticity solution for a thin rectangular slab. In addition, the elasticity results are used to verify the accuracy of the plate theory. Statics, dynamics as well as stability of plates are dealt with. Besides a lucid explanation of the theory, exact and approximate solution methodologies are discussed. The approach adopted throughout--with emphasis on close correspondence with the three-dimensional theory of elasticity, and on the implications of each assumption of the plate theory--enables the reader to easily progress on to the study of state-of-the-art topics such as geometric and material nonlinearities, refined plate theories accounting for warping and stretching of the normal and laminated construction and material orthotropy typical of fibre-reinforced composites.
Book Synopsis Mathematical Methods for Elastic Plates by : Christian Constanda
Download or read book Mathematical Methods for Elastic Plates written by Christian Constanda and published by Springer. This book was released on 2014-06-24 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers and aircraft. This book employs two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process of bending than Kirchhoff’s classical one. The first method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on the basis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hölder continuous and Hölder continuously differentiable) functions. The second technique rewrites the differential system in terms of complex variables and fully integrates it, expressing the solution as a combination of complex analytic potentials. The last chapter develops a generalized Fourier series method closely connected with the structure of the system, which can be used to compute approximate solutions. The numerical results generated as an illustration for the interior Dirichlet problem are accompanied by remarks regarding the efficiency and accuracy of the procedure. The presentation of the material is detailed and self-contained, making Mathematical Methods for Elastic Plates accessible to researchers and graduate students with a basic knowledge of advanced calculus.
Book Synopsis A Variational Principle for Reconstruction of Elastic Deformations in Shear Deformable Plates and Shells by : Alexander Tessler
Download or read book A Variational Principle for Reconstruction of Elastic Deformations in Shear Deformable Plates and Shells written by Alexander Tessler and published by . This book was released on 2003 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Methods in Science and Engineering by : Christian Constanda
Download or read book Integral Methods in Science and Engineering written by Christian Constanda and published by Springer Science & Business Media. This book was released on 2008 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The physical world is studied by means of mathematical models, which consist of differential, integral, and integro-differential equations accompanied by a large assortment of initial and boundary conditions. In certain circumstances, such models yield exact analytic solutions. When they do not, they are solved numerically by means of various approximation schemes. Whether analytic or numerical, these solutions share a common feature: they are constructed by means of the powerful tool of integration—the focus of this self-contained book. An outgrowth of the Ninth International Conference on Integral Methods in Science and Engineering, this work illustrates the application of integral methods to diverse problems in mathematics, physics, biology, and engineering. The thirty two chapters of the book, written by scientists with established credentials in their fields, contain state-of-the-art information on current research in a variety of important practical disciplines. The problems examined arise in real-life processes and phenomena, and the solution techniques range from theoretical integral equations to finite and boundary elements. Specific topics covered include spectral computations, atmospheric pollutant dispersion, vibration of drilling masts, bending of thermoelastic plates, homogenization, equilibria in nonlinear elasticity, modeling of syringomyelia, fractional diffusion equations, operators on Lipschitz domains, systems with concentrated masses, transmission problems, equilibrium shape of axisymmetric vesicles, boundary layer theory, and many more. Integral Methods in Science and Engineering is a useful and practical guide to a variety of topics of interest to pure and applied mathematicians, physicists, biologists, and civil and mechanical engineers, at both the professional and graduate student level.
Book Synopsis On the Theory of Transverse Bending of Elastic Plates by : E. Reissner
Download or read book On the Theory of Transverse Bending of Elastic Plates written by E. Reissner and published by . This book was released on 1975 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Departing from a self-contained two-dimensional formulation of the linear theory problem of transverse bending plates, three distinct topics are considered. The first of these concerns the integration problem for the case of orthotropy, specifically in regard to the factorization of a certain sixth-order master-equation. The second topic concerns the boundary layer aspects of contracted or reduced boundary conditions for the interior solution contribution for the case of isotropic plates. The analysis of this is based on a new form of the well known general solution in terms of a deflection and a stress function variable, with this new form making it possible to distinguish between first- and second-order transverse shear deformation effects; the former being associated with the edge zone and the latter with the interior domain of the plate, with the shear correction terms for the interior being generalizations of the Timoshenko shear correction terms for beams. The third topic is a new system of contracted boundary conditions, both for the stress and for the displacement boundary value problem, in such a way that first-order transverse shear deformation effects are explicitly incorporated in the interior-domain solution contribution, without the necessity of a simultaneous determination of the edge-zone solution contribution. (Author).
Book Synopsis The Generalized Fourier Series Method by : Christian Constanda
Download or read book The Generalized Fourier Series Method written by Christian Constanda and published by Springer Nature. This book was released on 2020-11-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains in detail the generalized Fourier series technique for the approximate solution of a mathematical model governed by a linear elliptic partial differential equation or system with constant coefficients. The power, sophistication, and adaptability of the method are illustrated in application to the theory of plates with transverse shear deformation, chosen because of its complexity and special features. In a clear and accessible style, the authors show how the building blocks of the method are developed, and comment on the advantages of this procedure over other numerical approaches. An extensive discussion of the computational algorithms is presented, which encompasses their structure, operation, and accuracy in relation to several appropriately selected examples of classical boundary value problems in both finite and infinite domains. The systematic description of the technique, complemented by explanations of the use of the underlying software, will help the readers create their own codes to find approximate solutions to other similar models. The work is aimed at a diverse readership, including advanced undergraduates, graduate students, general scientific researchers, and engineers. The book strikes a good balance between the theoretical results and the use of appropriate numerical applications. The first chapter gives a detailed presentation of the differential equations of the mathematical model, and of the associated boundary value problems with Dirichlet, Neumann, and Robin conditions. The second chapter presents the fundamentals of generalized Fourier series, and some appropriate techniques for orthonormalizing a complete set of functions in a Hilbert space. Each of the remaining six chapters deals with one of the combinations of domain-type (interior or exterior) and nature of the prescribed conditions on the boundary. The appendices are designed to give insight into some of the computational issues that arise from the use of the numerical methods described in the book. Readers may also want to reference the authors’ other books Mathematical Methods for Elastic Plates, ISBN: 978-1-4471-6433-3 and Boundary Integral Equation Methods and Numerical Solutions: Thin Plates on an Elastic Foundation, ISBN: 978-3-319-26307-6.
Book Synopsis Stationary Oscillations of Elastic Plates by : Gavin R. Thomson
Download or read book Stationary Oscillations of Elastic Plates written by Gavin R. Thomson and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations. Stationary Oscillations of Elastic Plates studies the latter in the context of stationary vibrations of thin elastic plates. The techniques presented here reduce the complexity of classical elasticity to a system of two independent variables, modeling problems of flexural-vibrational elastic body deformation with the aid of eigenfrequencies and simplifying them to manageable, uniquely solvable integral equations. The book is intended for an audience with a knowledge of advanced calculus and some familiarity with functional analysis. It is a valuable resource for professionals in pure and applied mathematics, and for theoretical physicists and mechanical engineers whose work involves elastic plates. Graduate students in these fields can also benefit from the monograph as a supplementary text for courses relating to theories of elasticity or flexural vibrations.
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.
Download or read book Dynamics of Plates written by J. S. Rao and published by Alpha Science Int'l Ltd.. This book was released on 1999 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic theories plates, variational principles and the use of delta operators that facilitate the derivation of differential equations and boundary conditions are explained in this book.
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 2004-04-22 with total page 268 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 Theory of Plates by : K. Chandrashekhara
Download or read book Theory of Plates written by K. Chandrashekhara and published by Universities Press. This book was released on 2001 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation by : Christian Constanda
Download or read book A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation written by Christian Constanda and published by Longman Scientific and Technical. This book was released on 1990 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Methods in Science and Engineering, Volume 2 by : Maria Eugenia Perez
Download or read book Integral Methods in Science and Engineering, Volume 2 written by Maria Eugenia Perez and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two volumes contain 65 chapters, which are based on talks presented by reputable researchers in the field at the Tenth International Conference on Integral Methods in Science and Engineering. The chapters address a wide variety of methodologies, from the construction of boundary integral methods to the application of integration-based analytic and computational techniques in almost all aspects of today's technological world. Both volumes are useful references for a broad audience of professionals, including pure and applied mathematicians, physicists, biologists, and mechanical, civil, and electrical engineers, as well as graduate students, who use integration as a fundamental technique in their research.
