General Theory of Heterogeneous Elastic Plates
Author: Girish Kumar Agrawal
Publisher:
Published: 1970
Total Pages: 346
ISBN-13:
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Theories of elastic plates
Author: V. Panc
Publisher: Springer Science & Business Media
Published: 1975-04-30
Total Pages: 750
ISBN-13: 9789028601048
DOWNLOAD EBOOKThe 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.
Vibrations in Heterogeneous Elastic Plates
Author: Peng-Chih Constance Yang
Publisher:
Published: 1962
Total Pages: 93
ISBN-13:
DOWNLOAD EBOOKA two-dimensional heterogeneous dynamic plate theory was deduced from the three-dimensional dynamic equations of elasticity. The heterogeneity of the material was considered to be only along the thickness coordinate of the plate. Approximations of shear deformations and of rotary inertia were included. A tenth order differential equation was derived. Five boundary conditions and proper initial conditions were obtained to insure an unique solution. It was recognized that the fact of coupling between stretching and bending in the heterogeneous plate led to this higher order (tenth) differential equation. The heterogeneous plate theory was specialized to cases of symmetrically laminated aeolotropic, orthotropic and isotropic plates respectively. A heterogeneous plate theory neglecting shear deformations was also deduced from the three-dimensional dynamic equation of elasticity. It was shown that the method of solving the forced vibration of a homogeneous plate of finite length could be extended to a heterogeneous plate. (Author).
Scientific and Technical Aerospace Reports
Author:
Publisher:
Published: 1994
Total Pages: 836
ISBN-13:
DOWNLOAD EBOOKNonlinear Analysis of Structures (1997)
Author: Muthukrishnan Sathyamoorthy
Publisher: CRC Press
Published: 2017-11-22
Total Pages: 548
ISBN-13: 1351359819
DOWNLOAD EBOOKNonlinear 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.
An Introduction to the Mathematical Theory of Vibrations of Elastic Plates
Author: Raymond David Mindlin
Publisher: World Scientific
Published: 2006
Total Pages: 211
ISBN-13: 9812703810
DOWNLOAD EBOOKThis 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.
Applied Mechanics Reviews
Author:
Publisher:
Published: 1974
Total Pages: 276
ISBN-13:
DOWNLOAD EBOOKRecent Developments in Anisotropic Heterogeneous Shell Theory
Author: Alexander Ya. Grigorenko
Publisher: Springer
Published: 2015-12-30
Total Pages: 129
ISBN-13: 981100353X
DOWNLOAD EBOOKThis volume focuses on the relevant general theory and presents some first applications, namely those based on classical shell theory. After a brief introduction, during which the history and state-of-the-art are discussed, the first chapter presents the mechanics of anisotropic heterogeneous shells, covering all relevant assumptions and the basic relations of 3D elasticity, classical and refined shell models. The second chapter examines the numerical techniques that are used, namely discrete orthogonalization, spline-collocation and Fourier series, while the third highlights applications based on classical theory, in particular, the stress-strain state of shallow shells, non-circular shells, shells of revolution, and free vibrations of conical shells. The book concludes with a summary and an outlook bridging the gap to the second volume.
Theory and Analysis of Elastic Plates and Shells
Author: J. N. Reddy
Publisher: CRC Press
Published: 2006-11-20
Total Pages: 561
ISBN-13: 0849384168
DOWNLOAD EBOOKBecause 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
Theories of elastic plates
Author: V. Panc
Publisher: Springer
Published: 2014-01-14
Total Pages: 0
ISBN-13: 9789401019064
DOWNLOAD EBOOKThe 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.
