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Nonlinear Theory of Elastic Plates

Nonlinear Theory of Elastic Plates
A Book

by Anh Le Van

  • Publisher : Elsevier
  • Release : 2017-05-31
  • Pages : 212
  • ISBN : 0081023596
  • Language : En, Es, Fr & De
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Nonlinear Theory of Elastic Plates provides the theoretical materials necessary for the three plate models—Cosserat plates, Reissner-Mindlin plates and Kirchhoff-Love plates— in the context of finite elastic deformations. One separate chapter is devoted to the linearized theory of Kirchhoff-Love plates, which allows for the study of vibrations of a pre-stressed plate and the static buckling of a plate. All mathematical results in the tensor theory in curvilinear coordinates necessary to investigate the plate theory in finite deformations are provided, making this a self-contained resource. Presents the tricky process of linearization, which is rarely dealt with, but explained in detail in a separate chapter Organized in a mathematical style, with definitions, hypotheses, theorems and proofs clearly stated Presents every theorem with its accompanying hypotheses, enabling the reader to quickly recognize the conditions of validity in results

A Nonlinear Theory for Thin Elastic Plates

A Nonlinear Theory for Thin Elastic Plates
A Book

by Jatin M. Anadkat,Youngstown State University. Rayen School of Engineering

  • Publisher : Unknown Publisher
  • Release : 1972
  • Pages : 130
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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The Effect of Shear Deformation and Transverse Warping in the Nonlinear Theory of Elastic Plates

The Effect of Shear Deformation and Transverse Warping in the Nonlinear Theory of Elastic Plates
A Book

by Juan C. Simo,James M. Kelly,Robert L. Taylor

  • Publisher : Unknown Publisher
  • Release : 1983
  • Pages : 33
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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A Nonlinear Theory of Thin Elastic Plates in Orthogonal Curvilinear Coordinates

A Nonlinear Theory of Thin Elastic Plates in Orthogonal Curvilinear Coordinates
A Book

by Amnuayporn Siriaksorn

  • Publisher : Unknown Publisher
  • Release : 1974
  • Pages : 74
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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An Introduction to the Mathematical Theory of Vibrations of Elastic Plates

An Introduction to the Mathematical Theory of Vibrations of Elastic Plates
A Book

by Raymond David Mindlin,Jiashi Yang

  • Publisher : World Scientific
  • Release : 2006
  • Pages : 190
  • ISBN : 9812703810
  • Language : En, Es, Fr & De
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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.

Linear Theories of Elasticity and Thermoelasticity

Linear Theories of Elasticity and Thermoelasticity
Linear and Nonlinear Theories of Rods, Plates, and Shells

by Clifford Truesdell

  • Publisher : Springer
  • Release : 2013-12-17
  • Pages : 745
  • ISBN : 3662397765
  • Language : En, Es, Fr & De
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Influence of Large Amplitudes on Flexural Motions of Elastic Plates

Influence of Large Amplitudes on Flexural Motions of Elastic Plates
A Book

by George Herrmann

  • Publisher : Unknown Publisher
  • Release : 1956
  • Pages : 45
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Starting with the fundamental equations of the general three-dimensional nonlinear theory of elasticity for the case of small elongations and shears but moderately large rotations, a set of plate equations of motiion is derived for an isotropic material obeying linear Hooke's law. Certain assumptions as to plate displacements are made at the outset. The resulting nonlinear plate theory of motion, valid for large deflections, is discussed in the light of the three-dimensional theory and other nonlinear plate theories, in particular, the static Von Karman plate theory.

The Nonlinear Theory of Elastic Shells

The Nonlinear Theory of Elastic Shells
One Spatial Dimension

by A. Libai

  • Publisher : Elsevier
  • Release : 2012-12-02
  • Pages : 428
  • ISBN : 0323150810
  • Language : En, Es, Fr & De
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The Nonlinear Theory of Elastic Shells: One Spatial Dimension presents the foundation for the nonlinear theory of thermoelastic shells undergoing large strains and large rotations. This book discusses several relatively simple equations for practical application. Organized into six chapters, this book starts with an overview of the description of nonlinear elastic shell. This text then discusses the foundation of three-dimensional continuum mechanics that are relevant to the shell theory approach. Other chapters cover several topics, including birods, beamshells, and axishells that begins with a derivation of the equations of motion by a descent from the equations of balance of linear and rotational momentum of a three-dimensional material continuum. This book discusses as well the approach to deriving complete field equations for one- or two-dimensional continua from the integral equations of motion and thermodynamics of a three-dimensional continuum. The final chapter deals with the analysis of unishells. This book is a valuable resource for physicists, mathematicians, and scientists.

Vibrations of Elastic Plates

Vibrations of Elastic Plates
Linear and Nonlinear Dynamical Modeling of Sandwiches, Laminated Composites, and Piezoelectric Layers

by Yi-Yuan Yu

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 228
  • ISBN : 1461223385
  • Language : En, Es, Fr & De
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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.

Theory and Analysis of Elastic Plates and Shells, Second Edition

Theory and Analysis of Elastic Plates and Shells, Second Edition
A Book

by J. N. Reddy

  • Publisher : CRC Press
  • Release : 2006-11-20
  • Pages : 568
  • ISBN : 9780849384158
  • Language : En, Es, Fr & De
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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, up-to-date, and unified treatment of classical and shear deformation plates and shells, from the basic derivation of theories to analytical and numerical solutions. Revised and updated, this second edition incorporates new information in most chapters, along with some rearrangement of topics to improve the clarity of the overall presentation. The book presents new material on the theory and analysis of shells, featuring an additional chapter devoted to the topic. The author also includes new sections that address Castigliano's theorems, axisymmetric buckling of circular plates, the relationships between the solutions of classical and shear deformation theories, and the nonlinear finite element analysis of plates. The book provides many illustrations of theories, formulations, and solution methods, resulting in an easy-to-understand presentation of the topics. Like the previous edition, this book remains a suitable textbook for a course on plates and shells in aerospace, civil, and mechanical engineering curricula and continues to serve as a reference for industrial and academic structural engineers and scientists.

Foundations of the Nonlinear Theory of Elasticity

Foundations of the Nonlinear Theory of Elasticity
A Book

by V. V. Novozhilov

  • Publisher : Courier Corporation
  • Release : 1999-01-01
  • Pages : 233
  • ISBN : 9780486406848
  • Language : En, Es, Fr & De
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This is an essential book for students and academicians alike. In addition to discussing theory, topics include the connection between stresses and strains in an isotropic elastic body, the geometry of strain, and much more. Deductions are explained in the simplest, most intuitive manner for wide accessibility. 1953 edition.

Theory and Analysis of Elastic Plates and Shells

Theory and Analysis of Elastic Plates and Shells
A Book

by J. N. Reddy

  • Publisher : CRC Press
  • Release : 2006-11-20
  • Pages : 568
  • ISBN : 0849384168
  • Language : En, Es, Fr & De
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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

The Theory of Shells and Plates. Part II: Nonlinear Theories of Elastic Shells

The Theory of Shells and Plates. Part II: Nonlinear Theories of Elastic Shells
A Book

by P. M. Naghdi,CALIFORNIA UNIV BERKELEY DIV OF APPLIED MECHANICS.

  • Publisher : Unknown Publisher
  • Release : 1971
  • Pages : 241
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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The report, the second of two parts, deals with the nonlinear and the linear theories of elastic shells and plates. It represents continuation of Part I and again all developments are carried out both by direct approach (i.e., via the theory of an elastic surface) and from the three-dimensional equations. Chapter D contains derivations of constitutive equations, thermodynamical retrictions, material symmetries and related results for both the nonlinear and the linear theories of elastic shells and plates. The relationship and correspondence between the results derived from the three-dimensional theory and those obtained by direct approach is discussed and special attention is given to the determination of the constitutive coefficients of the linear theory by direct approach in Chapter E. (Author).

Stress Concentration about Curvilinear Holes in Physically Nonlinear Elastic Plates

Stress Concentration about Curvilinear Holes in Physically Nonlinear Elastic Plates
A Book

by Aleksandr Nikolaevich Guzʹ,Guriĭ Nikolaevich Savin,I. A. Tsurpal

  • Publisher : Unknown Publisher
  • Release : 1966
  • Pages : 14
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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An approximate solution method of plane physical nonlinear problems of stress concentration about curvilinear holes in thin plates made of a material subject to a nonlinear law of elasticity is given. The solutions are represented in the form of expansions in the small parameter mu and epsilon. The determination of the stress function F for a physically nonlinear elastic plate with a hole reduces for each approximation to the integration of nonlinear differential equations. Stress concentration about an elliptic hole is considered in zero, first, and second approximation. The coefficient of stress concentration kappa is found on the contour of the hole, depending nonlinearly on the tensile forces Rho, the ellipticity of the hole, and parameter lambda characterizing the mechanical properties of the material. Tables represent the values of the coefficient of stress concentration for various values of the parameters Rho, lambda and epsilon.

Nonlinear Vibrations and Stability of Shells and Plates

Nonlinear Vibrations and Stability of Shells and Plates
A Book

by Marco Amabili

  • Publisher : Cambridge University Press
  • Release : 2008-01-14
  • Pages : 129
  • ISBN : 1139469029
  • Language : En, Es, Fr & De
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This unique book explores both theoretical and experimental aspects of nonlinear vibrations and stability of shells and plates. It is ideal for researchers, professionals, students, and instructors. Expert researchers will find the most recent progresses in nonlinear vibrations and stability of shells and plates, including advanced problems of shells with fluid-structure interaction. Professionals will find many practical concepts, diagrams, and numerical results, useful for the design of shells and plates made of traditional and advanced materials. They will be able to understand complex phenomena such as dynamic instability, bifurcations, and chaos, without needing an extensive mathematical background. Graduate students will find (i) a complete text on nonlinear mechanics of shells and plates, collecting almost all the available theories in a simple form, (ii) an introduction to nonlinear dynamics, and (iii) the state of art on the nonlinear vibrations and stability of shells and plates, including fluid-structure interaction problems.

Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies

Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies
A Book

by Leonid M. Zubov

  • Publisher : Springer Science & Business Media
  • Release : 2008-09-11
  • Pages : 208
  • ISBN : 3540684301
  • Language : En, Es, Fr & De
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The author applies methods of nonlinear elasticity to investigate the defects in the crystal structure of solids such as dislocations and disclinations that characterize the plastic and strength properties of many materials. Contrary to the geometrically motivated nonlinear theory of dislocations continuously distributed over the body, nonlinear analysis of isolated dislocations and disclinations is less developed; it is given for the first time in this book, and in a form accessible to both students and researchers. The general theory of Volterra's dislocations in elastic media under large deformations is developed. A number of exact solutions are found. The nonlinear approach to investigating the isolated defects produces results that often differ qualitatively from those of the linear theory.

Shell and Membrane Theories in Mechanics and Biology

Shell and Membrane Theories in Mechanics and Biology
From Macro- to Nanoscale Structures

by Holm Altenbach,Gennadi I. Mikhasev

  • Publisher : Springer
  • Release : 2014-09-09
  • Pages : 321
  • ISBN : 331902535X
  • Language : En, Es, Fr & De
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This book presents the latest results related to shells characterize and design shells, plates, membranes and other thin-walled structures, a multidisciplinary approach from macro- to nanoscale is required which involves the classical disciplines of mechanical/civil/materials engineering (design, analysis, and properties) and physics/biology/medicine among others. The book contains contributions of a meeting of specialists (mechanical engineers, mathematicians, physicists and others) in such areas as classical and non-classical shell theories. New trends with respect to applications in mechanical, civil and aero-space engineering, as well as in new branches like medicine and biology are presented which demand improvements of the theoretical foundations of these theories and a deeper understanding of the material behavior used in such structures.

Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials

Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials
A Book

by Marco Amabili

  • Publisher : Cambridge University Press
  • Release : 2018-11-01
  • Pages : 129
  • ISBN : 1108577636
  • Language : En, Es, Fr & De
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This book presents the most recent advances on the mechanics of soft and composite shells and their nonlinear vibrations and stability, including advanced problems of modeling human vessels (aorta) with fluid-structure interaction. It guides the reader into nonlinear modelling of shell structures in applications where advanced composite and complex biological materials must be described with great accuracy. To achieve this goal, the book presents nonlinear shell theories, nonlinear vibrations, buckling, composite and functionally graded materials, hyperelasticity, viscoelasticity, nonlinear damping, rubber and soft biological materials. Advanced nonlinear shell theories, not available in any other book, are fully derived in a simple notation and are ready to be implemented in numerical codes. The work features a blend of the most advanced theory and experimental results, and is a valuable resource for researchers, professionals and graduate students, especially those interested in mechanics, aeronautics, civil structures, materials, bioengineering and solid matter at different scales.

Refined Dynamical Theories of Beams, Plates and Shells and Their Applications

Refined Dynamical Theories of Beams, Plates and Shells and Their Applications
Proceedings of the Euromech-Colloquium 219

by Isaac Elishakoff,Horst Irretier

  • Publisher : Springer Science & Business Media
  • Release : 2013-03-12
  • Pages : 436
  • ISBN : 3642830404
  • Language : En, Es, Fr & De
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As is known, classical theories of vibration of the most fre quently encountered structural elements (e. g. , beams, plates and shells) disregard the effects of the shear deformation and rotary inertia. Refined theories, with these effects taken into account, have been pioneered by Bresse, Lord Rayleigh, Timoshenko, Eric Reissner, Mindlin and others. These refined theories have been fruitfully applied in recent decades in both theoretical and prac tical solid mechanics problems. The European Mechanics Committee approved holding EURO~illCH Colloquium 219 on "Refined Dynamical Theories of Beams, Plates and Shells and Their Applications" for reviewing the recent devel opments, providing guidelines for future investigations and presenting a forum for current work of younger researchers. The Colloquium was held during September 23 - 26, 1986, at the Uni versitat-Gesamthochschule Kassel, in the city of Kassel, Federal Republic of Germany. 45 Representatives of academia and industry, from nine European countries, as well as from Israel, USA and India participated in this Colloquium. IV 36 lectures were presented during the five sessions: Session A: Theory of Vibrations of Plates and Shells Session B: Various Approaches for Dynamical Problems of Beams Session C: Random Vibrations and Dynamic Stability Session D: Vibrations of Composite Structures Session E: Special Dynamical Problems of Beams, Plates and Shells The papers in this volums were divided into two parts: papers of invited keynote lectures and those of the invited contributed lectures.

Nonlinear Analysis of Structures (1997)

Nonlinear Analysis of Structures (1997)
A Book

by Muthukrishnan Sathyamoorthy

  • Publisher : CRC Press
  • Release : 2017-11-22
  • Pages : 640
  • ISBN : 1351359819
  • Language : En, Es, Fr & De
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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.