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Author: L. G. Jaeger
Publisher: Elsevier
ISBN: 1483147002
Category : Technology & Engineering
Languages : en
Pages : 119
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Book Description
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.
Author: L. G. Jaeger
Publisher: Elsevier
ISBN: 1483147002
Category : Technology & Engineering
Languages : en
Pages : 119
Get Book Here
Book Description
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.
Author: Raymond David Mindlin
Publisher: World Scientific
ISBN: 9812772499
Category : Technology & Engineering
Languages : en
Pages : 211
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Book Description
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.
Author: Kaza Vijayakumar
Publisher: Springer Nature
ISBN: 9813342102
Category : Technology & Engineering
Languages : en
Pages : 149
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Book Description
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: Chyanbin Hwu
Publisher: Springer Science & Business Media
ISBN: 1441959157
Category : Technology & Engineering
Languages : en
Pages : 678
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Book Description
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.
Author: Eduard Ventsel
Publisher: CRC Press
ISBN: 9780203908723
Category : Mathematics
Languages : en
Pages : 688
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Book Description
Presenting recent principles of thin plate and shell theories, this book emphasizes novel analytical and numerical methods for solving linear and nonlinear plate and shell dilemmas, new theories for the design and analysis of thin plate-shell structures, and real-world numerical solutions, mechanics, and plate and shell models for engineering appli
Author: J. D. Kaplunov
Publisher: Academic Press
ISBN: 0123975905
Category : Mathematics
Languages : en
Pages : 241
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Book Description
This text is a study of the asymptotic approximations of the 3-D dynamical equations of elasticity in the case of thin elastic shells of an arbitrary shape.
Author: M.L. Gambhir
Publisher: Springer Science & Business Media
ISBN: 3662099969
Category : Technology & Engineering
Languages : en
Pages : 542
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Book Description
This advanced and graduate-level text and self-tutorial teaches readers to understand and to apply analytical design principles across the breadth of the engineering sciences. Emphasizing fundamentals, the book addresses the stability of key engineering elements such as rigid-body assemblage, beam-column, beam, rigid frame, thin plate, arch, ring, and shell. Each chapter contains numerous worked-out problems that clarify practical application and aid comprehension of the basics of stability theory, plus end-of-chapter review exercises. Others key features are the citing and comparison of different national building standards, use of non-dimensional parameters, and many tables with much practical data and simplified formula, that enable readers to use them in the design of structural components. First six chapters most suitable for undergraduate-level study and remaining chapters for graduate-level courses.
Author: Christian Constanda
Publisher: Springer
ISBN: 1447164342
Category : Mathematics
Languages : en
Pages : 213
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Book Description
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.
Author: A.P.S. Selvadurai
Publisher: Springer Science & Business Media
ISBN: 3662092050
Category : Technology & Engineering
Languages : en
Pages : 713
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Book Description
This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.
Author: Basile Audoly
Publisher: Oxford University Press
ISBN: 0198506252
Category : Mathematics
Languages : en
Pages : 597
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Book Description
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.
