Elastic shells are pervasive in everyday life. Examples of these thin-walled structures range from automobile hoods to basketballs, veins, arteries and soft drink cans. This book explains shell theory, with numerous examples and applications. As a second edition, it not only brings all the material of the first edition entirely up to date, it also adds two entirely new chapters on general shell theory and general membrane theory. Aerospace, mechanical and civil engineers, as well as applied mathematicians, will find this book a clearly written and thorough information source on shell theory.

This paper provides a comprehensive description of the mechanical response of freestanding circular elastic films subjected to point and pressure loads. Regimes of behavior, such as plate, linear membrane, and nonlinear membrane, are identified in terms of two dimensionless variables that allow the creation of a single map that indicates appropriate closed-form solutions. This map provides a theoretical framework to design experiments and interpret film behavior for all orders of magnitude of: film thickness-to-span ratio, deflection, loads, prestretch, and elastic properties. The normalization approach provides the means to quickly identify appropriate simplifications to the nonlinear governing equations, and identify applicable analytical solutions. Numerical results are used to illustrate behavior in transition regions, e.g., the transition for a given plate thickness from small to large deflections under increasing load. Critical loads, thickness and prestretch are identified which indicate when asymptotic plate or membrane solutions are accurate. Asymptotic and numerical results are presented which illustrate finite-sized regions of bending-influenced deformation near point loads and clamped edges. Theoretical predictions for the width of these regions enable us to estimate the validity of analytical strain distributions, and in turn the maximum strains in the film. These results help avoiding brittle fracture or ductile yielding of the film by identifying physical parameters that limit strains to an acceptable level.

The authors make no attempt to summarize the results available in this area through approximate solutions of various kinds to the 3-D field equations. Nor do they present, for readers prepared to utilize modern computer techniques, finite element, boundary integral, and other numerical techniques for obtaining such solutions. Finally, it seems to the reviewer that there is little added to this book by an "Introductory Chapter" of approximately 40 pages, authored by Sih, on the "strain-energy-density factor" theory of crack growth and its extension to 3-D problems. First, the chapter seems extraneous in the sense that nothing else in the book touches on theories of crack growth. But this theory, while presented with evident enthusiasm, seems to derive from no self-consistent or physically plausible description of the crack growth process. Instead, failure is assumed to occur when a local minimum value of the energy density, at some given radius from the crack tip, reaches a critical value. Why the energy density, and especially, a local minimum of it, should be chosen is unclear enough. But the function does indeed have a local minimum, in general, and it seems disconcerting to take as critical a value of the energy density for which both greater and lesser values occur at other points at the same given radius from the crack tip. Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures.

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