Boundary Element Analysis of Plates and Shells

 Boundary Element Analysis of Plates and Shells

Boundary Element Analysis of Plates and Shells

Plates and shells constitute a large class of surface type of
structures with one of their dimensions, their thickness, much smaller than the other two dimensions. The analysis of the behavior of these structures under static and dynamic loads is of great interest to scientists and engineers both from the theoretical and the practical viewpoint. Indeed, the analysis of these structures represents a very challenging and attractive theoretical problem, as well as a problem of great practical significance, associated with applications in many enginee-
ring fields, such as civil, mechanical, aerospace, etc.

It is well known that numberical methods of solution, such as the Finite Difference Method (FDM) and especially the Finite Element Method (FEM) are the only practical means for analysing this class of surface structures under complex boundary and loading conditions and/or realistic material behavior.

During the last 20 years the Boundary Element Method (BEM) has emerged as a powerful tool for the numerical solution of various complex problems of mechanics. This method has some distinct advantages over domain type techniques, such as the FDM and the FEM for a wide class of structural analysis problems. Information concerning the application of the BEM to plate short the BEM and shell analysis can be found in the form of rather sections or chapters in a number of books devoted to and its applications to various fields of engineering science and mechanics. These sections or chapters, however, deal mainly with static analysis of plates and shells and do not cover the more recent exciting developments in the area.
No specific book dealing exclusively with the analysis of
plates and shells by the BEM and covering all the aspects of their behavior up to date exists in the literature.
The present book represents an effort to fill this gap in the
literature by combining tutorial and state-of-the-art aspects of the BEM as applied to plates and shells. It aims at informing scientists and engineers engaged in the analysis of surface type of structures, about the use and the advantages of this technique, the most recent developments in the field and the pertinent literature for further study. The reader is expected to have a basic knowledge of plate and shell theory and applied mathematics.

The book is divided into nine chapters, written by persons
very well known for their contributions in the field, which
cover all the aspects of plate and shell analysis by the BEM
existing to this date in the literature. More specifically,
chapter one provides a comprehensive treatment of the static analysis of linear elastic Kirchhoff plates and plate systems by the conventional direct BEM and serves as an introduction to the basic concepts and ideas of the method. chapter two considers free and forced vibrations of linear elastic plates and plate systems by the conventional direct BEM and the domain (field) BEM in the time and frequency domains. Static and dynamic analysis of linear elastic Vlasov-Reisner shallow shells by the direct BEM and the domain (field) BEM in the time and frequency domains is the subject of chapter three. Nonlinearities are discussed in the next two chapters. Static and dynamic analysis of plates and shells exhibiting large

elastic deformations and inelastic material behavior are discussed in chapter four and five, respectively. Linear and nonlinear stability analysis of plates, plate systems and shallow shells is described in chapter six. Chapter seven deals with some special methods for static and dynamic analysis of elastic plates including the indirect BEM, the BEM based on biharmonic analysis and the BEM employing finite domain Green's functions. The special case of Reissner-Mindlin plates under static and dynamic conditions is taken up in chapter eight.

Finally, chapter nine discusses two boundary type of methods for analysing elastic plates and shells under static and dynamic conditions, namely the boundary collocation and briefly the edge function method.

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