An Introduction to the Mathematical Theory of Vibrations of Elastic Plates

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: 9812772499

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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.


Nonlinear Analysis of Structures (1997)

Nonlinear Analysis of Structures (1997)

Author: Muthukrishnan Sathyamoorthy

Publisher: CRC Press

Published: 2017-11-22

Total Pages: 548

ISBN-13: 1351359819

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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.


Recent Developments in Anisotropic Heterogeneous Shell Theory

Recent Developments in Anisotropic Heterogeneous Shell Theory

Author: Alexander Ya. Grigorenko

Publisher: Springer

Published: 2015-12-30

Total Pages: 129

ISBN-13: 981100353X

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This 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

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

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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


Principles of Composite Material Mechanics, Second Edition

Principles of Composite Material Mechanics, Second Edition

Author: Ronald F. Gibson

Publisher: CRC Press

Published: 2007-05-30

Total Pages: 610

ISBN-13: 1420014242

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Extensively updated and maintaining the high standard of the popular original, Principles of Composite Material Mechanics, Second Edition reflects many of the recent developments in the mechanics of composite materials. It draws on the decades of teaching and research experience of the author and the course material of the senior undergraduate and graduate level classes he has taught. New and up-to-date information throughout the text brings modern engineering students everything they need to advance their knowledge of the evermore common composite materials. The introduction strengthens the book’s emphasis on basic principles of mechanics by adding a review of the basic mechanics of materials equations. New appendices cover the derivations of stress equilibrium equations and the strain–displacement relations from elasticity theory. Additional sections address recent applications of composite mechanics to nanocomposites, composite grid structures, and composite sandwich structures. More detailed discussion of elasticity and finite element models have been included along with results from the recent World Wide Failure Exercise. The author takes a phenomenological approach to illustrate linear viscoelastic behavior of composites. Updated information on the nature of fracture and composite testing includes coverage of the finite element implementation of the Virtual Crack Closure technique and new and revised ASTM standard test methods. The author includes updated and expanded material property tables, many more example problems and homework exercises, as well as new reference citings throughout the text. Requiring a solid foundation in materials mechanics, engineering, linear algebra, and differential equations, Principles of Composite Materials Mechanics, Second Edition provides the advanced knowledge in composite materials needed by today’s materials scientists and engineers.


Principles of Composite Material Mechanics, Third Edition

Principles of Composite Material Mechanics, Third Edition

Author: Ronald F. Gibson

Publisher: CRC Press

Published: 2011-09-21

Total Pages: 686

ISBN-13: 1439850054

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Principles of Composite Material Mechanics, Third Edition presents a unique blend of classical and contemporary mechanics of composites technologies. While continuing to cover classical methods, this edition also includes frequent references to current state-of-the-art composites technology and research findings. New to the Third Edition Many new worked-out example problems, homework problems, figures, and references An appendix on matrix concepts and operations Coverage of particle composites, nanocomposites, nanoenhancement of conventional fiber composites, and hybrid multiscale composites Expanded coverage of finite element modeling and test methods Easily accessible to students, this popular bestseller incorporates the most worked-out example problems and exercises of any available textbook on mechanics of composite materials. It offers a rich, comprehensive, and up-to-date foundation for students to begin their work in composite materials science and engineering. A solutions manual and PowerPoint presentations are available for qualifying instructors.


Stress Waves in Solids

Stress Waves in Solids

Author: Herbert Kolsky

Publisher: Courier Corporation

Published: 1963-01-01

Total Pages: 226

ISBN-13: 0486610985

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The most readable survey of the theoretical core of current knowledge available. The author gives a concise account of the classical theory necessary to an understanding of the subject and considers how this theory has been extended to solids.


Recent Developments in the Theory of Shells

Recent Developments in the Theory of Shells

Author: Holm Altenbach

Publisher: Springer Nature

Published: 2019-09-25

Total Pages: 799

ISBN-13: 3030177475

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This book commemorates the 80th birthday of Prof. W. Pietraszkiewicz, a prominent specialist in the field of general shell theory. Reflecting Prof. Pietraszkiewicz’s focus, the respective papers address a range of current problems in the theory of shells. In addition, they present other structural mechanics problems involving dimension-reduced models. Lastly, several applications are discussed, including material models for such dimension-reduced structures.