This book is a greatly expanded version of parts of our monograph, “Nonlinear Elastic Shell Theory,” that appeared on pages 271-371 of Volume 23 of Advances in Applied Mechanics (J. W. Hutchinson & T. Y. Wu, eds.), Academic Press, 1983. We have added several new chapters and rewritten or supplemented others extensively. Discussions of stability and variational principles, which were omitted from the monograph for lack of space, are included here. Furthermore, some material on load potentials, nonlinear constitutive laws, thermodynamics (as applied to shells), and boundary conditions is original. Space, time, and our proclivities have prevented us from discussing numerical solutions of shell equations, an important area that needs to be surveyed, summarized, and streamlined. The state of the art may be gleaned from books by Hinton & Owen, Hughes & Hinton, and Bushnell.

This book has two main goals: to lay a foundation for the nonlinear theory of thermoelastic shells undergoing large rotations and large strains and to present, early on, relatively simple equations for practical application. We have tried to write for those who know some continuum mechanics but little shell theory, but we think that experts will find here much that is novel—in presentation if not in content. Thus, after an introductory chapter that describes what we mean by a nonlinear elastic shell and spells out our approach, we expose, in the next chapter, the bedrock of three-dimensional continuum mechanics.