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This book attempts to bring the essence of shell structures within the grasp of engineers. It tackles the fundamental question of how bending and stretching effects combine and interact in shell structures from a physical point of view; and shows that this approach leads to an understanding of the structural mechanics of shells in general.
Through several centuries there has been a lively interaction between mathematics and mechanics. On the one side, mechanics has used mathemat ics to formulate the basic laws and to apply them to a host of problems that call for the quantitative prediction of the consequences of some action. On the other side, the needs of mechanics have stimulated the development of mathematical concepts. Differential calculus grew out of the needs of Newtonian dynamics; vector algebra was developed as a means . to describe force systems; vector analysis, to study velocity fields and force fields; and the calcul~s of variations has evolved from the energy principles of mechan ics. In recent times the theory of tensors has attracted the attention of the mechanics people. Its very name indicates its origin in the theory of elasticity. For a long time little use has been made of it in this area, but in the last decade its usefulness in the mechanics of continuous media has been widely recognized. While the undergraduate textbook literature in this country was becoming "vectorized" (lagging almost half a century behind the development in Europe), books dealing with various aspects of continuum mechanics took to tensors like fish to water. Since many authors were not sure whether their readers were sufficiently familiar with tensors~ they either added' a chapter on tensors or wrote a separate book on the subject.
Plate and shell theories experienced a renaissance in recent years. The potentials of smart materials, the challenges of adaptive structures, the demands of thin-film technologies and more on the one hand and the availability of newly developed mathematical tools, the tremendous increase in computer facilities and the improvement of commercial software packages on the other caused a reanimation of the scientific interest. In the present book the contributions of the participants of the EUROMECH Colloquium 444 "Critical Review of the Theories of Plates and Shells and New Applications" have been collected. The aim was to discuss the common roots of different plate and shell approaches, to review the current state of the art, and to develop future lines of research. Contributions were written by scientists with civil and mechanical engineering as well as mathematical and physical background.
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
Euromech-Colloquium Nr. 165 The shell-theory development has changed its emphasis during the last two decades. Nonlinear problems have become its main motive. But the analysis was until recently predominantly devoted to shells designed for strength and stiffness. Nonlinearity is here relevant to buckling, to intensively vary able stress states. These are (with exception of some limit cases) covered by the quasi-shallow shell theory. The emphasis of the nonlinear analysis begins to shift further - to shells which are designed for and actually capable of large elastic displacements. These shells, used in industry for over a century, have been recently termedj1exible shells. The European Mechanics Colloquium 165. was concerned with the theory of elastic shells in connection with its applications to these shells. The Colloquium was intended to discuss: 1. The formulations of the nonlinear shell theory, different in the generality of kine matic hypothesis, and in the choice of dependent variables. 2. The specialization of the shell theory for the class of shells and the respective elastic stress states assuring flexibility. 3. Possibilities to deal with the complications of the buckling analysis of flexible shells, caused by the precritial perturbations of their shape and stress state. 4. Methods of solution appropriate for the nonlinear flexible-shell problems. 5. Applications of the theory. There were 71 participants the sessions were presided over (in that order) by E. Reissner, J. G. Simmonds, W. T. Koiter, R. C. Tennyson, F. A. Emmerling, E. Rarnm, E. L. Axelrad.
Noted for its practical, accessible approach to senior and graduate-level engineering mechanics, Plates and Shells: Theory and Analysis is a long-time bestselling text on the subjects of elasticity and stress analysis. Many new examples and applications are included to review and support key foundational concepts. Advanced methods are discussed and analyzed, accompanied by illustrations. Problems are carefully arranged from the basic to the more challenging level. Computer/numerical approaches (Finite Difference, Finite Element, MATLAB) are introduced, and MATLAB code for selected illustrative problems and a case study is included.
Vibrations drive many engineering designs in today's engineering environment. There has been an enormous amount of research into this area of research over the last decade. This book documents some of the latest research in the field of vibration of composite shells and plates filling a much-needed gap in the market. Laminated composite shells have many engineering applications including aerospace, mechanical, marine and automotive engineering. This book makes an ideal reference for researchers and practicing engineers alike. - The first book of its kind - Documents 10 years of research in the field of composite shells - Many Engineering applications
The design of many structures such as pressure vessels, aircrafts, bridge decks, dome roofs, and missiles is based on the theories of plates and shells. The degree of simplification needed to adopt the theories to the design of various structures depends on the type of structure and the re quired accuracy of the results. Hence, a water storage tank can be satis factorily designed using the membrane shell theory, which disregards all bending moments, whereas the design of a missile casing requires a more precise analysis in order to minimize weight and materials. Similarly, the design of a nozzle-to-cylinder junction in a nuclear reactor may require a sophisticated finite element analysis to prevent fatigue failure while the same junction in an air accumulator in a gas station is designed by simple equations that satisfy equilibrium conditions. Accordingly, this book is written for engineers interested in the theories of plates and shells and their proper application to various structures. The examples given throughout the book subsequent to derivation of various theories are intended to show the engineer the level of analysis required to achieve a safe design with a given degree of accuracy. The book covers three general areas. These are: bending of plates; membrane and bending theories of shells; and buckling of plates and shells. Bending of plates is discussed in five chapters. Chapters 1 and 2 cover rectangular plates with various boundary and loading conditions.
Over the past decade or so much has been written on the various attempts to produce efficient, accurate and reliable Mindlin plate finite elements. In the late sixties, a degenerated, Mindlin-type, curved shell element was developed and subsequently many improvements in such elements have been made. Reliability and efficiency in use has always been a major objective. Degenerated shell elements have enjoyed widespread popularity despite certain potential defects, including shear and membrane lock ing behaviour and spurious mechanisms. After introducing the basic foundations of Mindlin-type elements, this book describes these defects and also gives the reasons for their occurrence. Furthermore, the author proposes an approach to overcome these defects. A series of linear benchmark tests are proposed to illustrate the performance of the assumed strain element formulations. The formula tions and applications for material non-linearity are also presented. Both isotropic and anisotropic material models are included together with the results for both static and transient dynamic analyses. Two associated programs are fully documented and provided on floppy discs with test examples. Source codes for the two associated programs are provided: one is for static analysis and the other for dynamic analysis, and the programs can be compiled and run on either a mini or mainframe coniputer via a terminal. The author hopes that this book may provide further impetus in the important research area of plate and shell element technology.