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- Release : 01 January 1970
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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,
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.
Reissue of Encyclopedia of Physics / Handbuch der Physik, Volume VIa The mechanical response of solids was first reduced to an organized science of fairly general scope in the nineteenth century. The theory of small elastic deformations is in the main the creation of CAUCHY, who, correcting and simplifying the work of NAVIER and POISSON, through an astounding application of conjoined scholarship, originality, and labor greatly extended in breadth the shallowest aspects of the treatments of par ticular kinds of bodies
Soft biological tissues often undergo large (nearly) elastic deformations that can be analyzed using the nonlinear theory of elasticity. Because of the varied approaches to nonlinear elasticity in the literature, some aspects of the subject may be difficult to appreciate. This book attempts to clarify and unify those treatments, illustrating the advantages and disadvantages of each through various examples in the mechanics of soft tissues. Applications include muscle, arteries, the heart, and embryonic tissues.
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
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
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
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
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
This book guides the reader into the modelling of shell structures in applications where advanced composite materials or complex biological materials must be described with great accuracy. A valuable resource for researchers, professionals and graduate students, it presents a variety of practical concepts, diagrams and numerical results.
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,
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
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,