This book deals with various aspects in relation with thin shell theory: general geometric formalism of shell theory, analysis of singularities, numerical computing of thin shell problems, mathematical considerations on boundary values problems.

This account of the theory of plates and shells is written primarily as a textbook for graduate students in mechanical and civil engineering.The unified treatment of shells of arbitrary shape is accomplished by tensor analysis. This useful tool is introduced in the first chapter, and no knowledge of advanced mathematical methods is required. The general theory developed in the first eight chapters is applied in the remaining part to thin elastic plates and shells with special emphasis on engineering methods and engineering applications. A number of detailed examples illustrate the theory.

This book commemorates the 80th birthday of Prof. W. Pietraszkiewicz, a prominent specialist in the field of general shell theory. Reflecting Prof. Pietraszkiewicz’s focus, the respective papers address a range of current problems in the theory of shells. In addition, they present other structural mechanics problems involving dimension-reduced models. Lastly, several applications are discussed, including material models for such dimension-reduced structures.

The objective of Volume III is to lay down the proper mathematical foundations of the two-dimensional theory of shells. To this end, it provides, without any recourse to any a priori assumptions of a geometrical or mechanical nature, a mathematical justification of two-dimensional nonlinear and linear shell theories, by means of asymptotic methods, with the thickness as the "small" parameter.

Introduction to the Theory of Shells provide a brief introduction to the foundations of shell theory, and to some of the important problems that can be tackled within the framework of shell theory. The book discusses topics on the Lamé problem and derivation of beam theory; the basic postulates, or assumptions of shell theory; membrane shells and the bending of circular cylinders; and axisymmetric vibrations of circular cylinders. Mathematicians and students of mathematics will find the book invaluable.