Description
This book deals with the mechanics and numerical simulations of plates and shells, which are flat and curved thin-walled structures, respectively (called shell structures for short in this book). They have very important applications as complete structures or structural elements in many branches of engineering. Examples of shell structures in civil and mechanical engineering include slabs, vaults, roofs, domes, chimneys, cooling towers, pipes, tanks, containers and pressure vessels; in shipbuilding – ship and submarine hulls, in the vehicle and aerospace industries – automobile bodies and tyres and the wings and fuselages of aeroplanes.
The scope of the book is limited to the presentation of the theory of elastic plates and shells undergoing small deformation (thus assuming linear constitutive and kinematic equations).
The book is aimed at the large international community of engineering students, university teachers, professional engineers and researchers interested in the mechanics of shell structures, as well as developers testing new simulation software.The book can be the basis of an intermediate-level course on (computational) mechanics of shell structures at the level of doctoral, graduate and undergraduate studies. The reader should have the basic knowledge of the strength of materials, theory of elasticity, structural mechanics and FEM technology; basic information in these areas is not repeated in the book.
The strength of the book results from the fact that it not only provides the theoretical formulation of fundamental problems of mechanics of plates and shells, but also several examples of analytical and numerical solutions for different types of shell structures.The book also contains some advanced aspects related to the stability analysis and a brief description of classical and modern finite element formulations for plates and shells, including the discussion of mixed/hybrid models and so-called locking phenomena.
The book contains a comprehensive presentation of the theory of elastic plates and shells, formulations and solutions of fundamental mechanical problems (statics, stability, free vibrations) for these structures using exact approaches and computational (approximate) methods, with emphasis on modern capabilities of the finite element (FE) technology. In the book we introduce a large number of examples that illustrate various physical phenomena associated with the behaviour of shell structures under external actions. Comparisons of analytical and numerical solutions are given for several benchmark tests.Thebook includes plenty of boxes and tables that contain sets of formulae or data and check values describing the examples.They help the reader to find and integrate the information provided and draw conclusions.
The authors are researchers and teachers from the Institute for Computational Civil Engineering of Cracow University of Technology.They have done research on structural mechanics for years, in particular on the theories and advanced computational methods for shell structures, and they also have a long history of teaching the subject to students and practitioners. The selection of the contents of the book is based on this experience. The motivation to write the present book has also come from the fact that there are no books that contain, in one volume, the foundation of the theory and solutions of selected problems using simultaneously analytical and numerical methods.
Following a sequence of subjects: mathematics, theoretical mechanics, strength of materials, structural mechanics, computer science, numerical methods and the finite elementmethod – we have developed a comprehensive course on themechanics of shell structures. This course contains: (i) discussion of the assumptions and limits of applicability of selected theories on which mathematical models are based, (ii) choice of a method to solve the problem efficiently, (iii) analytical and/or numerical calculations simulating physical phenomena or processes, (iv) confrontation of the results of theoretical and numerical analysis and (v) evaluation of the calculation methodology and results.