7R28. Thin Plates and Shells: Theory, Analysis, and Applications. - E Ventsel (Eng Sci and Mech Dept, Penn State, Univ Park PA 16802) and T Krauthammer (Protective Tech Center, Penn State, Univ Park PA 16802). Marcel Dekker, New York. 2001. 666 pp. ISBN 0-8247-0575-0. $175.00.

Reviewed by E Carrera (Dept of Aerospace Eng, Politecnico di Torino, Corso Duca Degli Abruzzi 24, Torino, 10129, Italy).

“Thin plates,” “thin shells,” and “thin plates and shells” are classical subjects for books. Eminent scientists, such as Vlasov, Flu¨gge, Novozhilov, Timoschenko, Washizu, Kraus, Gold’enveizer, Cicala, Librescu, Donnell, Vekua, and Leissa among others, have written milestone books on the topic. All of these books are, with no doubt, excellent sources for the analysis of two-dimensional structures. Most of these classical books have appeared in the middle of the last century and, in the same case each book states the point of view of each scientist on plate and shell theories. A few books on plates and shells are known which have been published in the recent past. Among these the book by Ventsel and Krauthammer is one of the most useful and exhaustive. It includes both plate and shell geometries as well as theories and solutions of practical problems. Ventsel and Krauthammer present several topics in a manner which results in a brilliant selection of different possible ways to see plates and shells as they are known by the classical books mentioned above. This book is a good synthesis of West and East Schools of knowledge on plates and shells. It is clearly written, self complete, and rich with examples as well as of applications to practical problems. The authors have shown their own ability in writing a book on plates and shells avoiding vectorial or tensorial notations which could introduce difficulties to beginners. The editorial form is quite well done: figures, plots, formulas, and texts are very well balanced in each chapter and on each page.

The book has been divided in two parts which deal with thin plates and thin shells, respectively. Each part quotes introduction, fundamentals, membrane and bending response, buckling, and vibrations. A brief description of the book’s layout is given below.

Part I is first considered. Chapter 1 offers a very interesting historical note on plates theories. Fundamentals of elasticity relations are recalled in a Cartesian reference system. Kirchhoff’s thin plate theory has been described in Chapter 2; governing equations are derived by using both elasticity relations and variational statements. Bending of rectangular plates are treated in Chapter 3; a large variety of practical problems have been solved by considering different geometries, boundary conditions and applied loadings. Chapter 4 has been devoted to circular plates. Polar coordinates have been preferred in this case. Other geometries, such as elliptical and triangular plates have been solved in Chapter 5. Approximated solution methods and their applications are discussed in Chapter 6 in which Finite Difference, Finite Element, and Boundary Element Methods are introduced and applied to two-dimensional flat structures. Advanced topics are addressed in Chapter 7; thermoelastic problems, stiffened plates, orthotropic behavior, refined theories accounting for transverse shear deformation effects, geometrically nonlinear behavior, layered, and sandwich plates are considered. Buckling of plates has been considered in Chapter 8; introductory concepts are first introduced, buckling of rectangular and circular plates are then solved by application of equilibrium and energy methods. Results are also given for stiffened, orthotropic, and sandwich plates. Large deflection and post-buckling response have also been treated in this chapter. Dynamic problems are considered in Chapter 9.

Thin shells theory and analysis begin with Chapter 10. This chapter introduces shell structure and makes an historical note on main shell theory contributions and developments. Concepts related to differential geometry of surfaces are given in Chapter 11. First and second fundamental forms are derived and particularized to several geometrical shell configurations (shell of revolution, cylindrical, and conical). Linear elasticity relations in curvilinear coordinates and in the framework of Kirchhoff-Love postulates are presented in Chapter 12. Membrane shell theories and applications are considered in Chapters 13 and 14, respectively. Methods, solution techniques, and results are presented for a large variety of problems, such as roof shell structures, liquid storage facilities, and pressurized vessels. So called moment theory has been addressed in Chapter 15 for circular cylindrical cases. The asymptotic integration method has been used to solve the differential equations of cylindrical shell subjected to general loadings. Solutions of particular cases are presented in the same chapter. Extension to shells of revolution is given in Chapter 16. Other well known approximated shell theories are discussed and applied in Chapter 17. The advanced topic already discussed in Chapter 8 for the plate cases, are extended to shells in Chapter 18. In addition, Chapter 18 gives details of the application of Newton’s Method to solve nonlinear problems. Buckling and vibration problems of shells are discussed in Chapters 19 and 20, respectively. Five Appendices close the book. The first one quotes useful data while the others detail some derivations which were not explicitly given in the previous chapters.

This reviewer’s opinion is Thin Plates and Shells: Theory, Analysis, and Applications by Ventsel and Krauthammer contains those basics and advanced arguments that should be known to any engineer or scientist who is supposed to work with plate and shell structures.