ISBN 0 521 47236 9 hardback) Shell structures or briefly shells are classical geometric approximations of three-dimensional solids in engineering science. There are countless applications of shells in modern technologies, but also nature during its evolution has early discovered a large variety of advantages of applying shells in fauna and flora.
Shell structures can be subjected to external loads and displacements or to internal strains. These effects may cause large displacement responses with or without structural instabilities, both in the static or in the dynamic regime. The monograph under consideration covers theoretical aspects and offers analytical solutions for many of these shell response phenomena. The volume represents the second and extended edition of an earlier book first published in 1988.
The monograph starts with a very short repetition of the theory of three-dimensional continuum thermomechanics, more or less in order to get the reader acquainted with the notation used throughout the text. The first pertinent chapter contains the mechanics of straight rods with cross-sections of bi-axial symmetry. Herein, their equation of motion in integral and differential form is presented, further their boundary conditions, then the weak form of the equation of motion and finally the principle of virtual work. The theory then is specified to elastic material behavior presenting several variational principles. The chapter is terminated by an outline of the theory of thermo-elastic rods.
Interestingly, all further chapters are composed in a very similar manner. Chapter 4 presents shells with beam-like response behavior, Chapter 5 those of revolution. Both chapters are supplemented by sections on stability phenomena of the respective shells. This treatise is followed by shells which are subjected only to one-dimensional states of strain; then a large chapter treats the nonlinear membrane theory of general shells including wrinkling phenomena. The volume finally ends with a chapter on bending theory of shells, formulated for a general shape of the middle surface.
Certainly this concept of the book is chosen in order to introduce the reader into the subject from the point of view of shell response phenomena, and by this it is a very valuable documentation of many existing analytical solutions which really provide insight into typical deformation behaviours. The aim of the book is clearly some proximity to practical applications, starting from relatively special cases of shells. Such a concept, necessarily, leads to repetitions. A considerably shorter and may be more modern way would have been a start with the derivation of a generally applicable shell theory for arbitrary mid-surfaces, and in a second step its specification to those special forms for which analytical solutions are available.
With reference to modern computer analysis the reviewers would have further expected a mathematically much rigorous derivation with respect to variational functionals as basis of numerical simulation concepts. Equations of motion, e.g., are derived from the three-dimensional equations of balance of momentum and of moment of momentum without introducing explicitly a kinematic hypothesis, named by the authors as constitutive assumptions. But any kinematic constraint, e.g., the Kirchhoff-Love-hypothesis, influences directly the strain-displacement-relations which in turn determine by the Gauss-Green-theorem the structure of the equations of motion consistent with the adopted kinematic assumptions. Such essential characteristics of any