This book is about the two most important aspects of plate and shell theories: (1) the foundations of these theories to serve as approximation of the corresponding elasticity solution, and (2) the unique feature of a static-geometric duality inherent in these theories. As an approximation of the elasticity solution for slender bodies, (the unproven) Saint-Venant's principle is usually invoked to justify the assignment of resultant force and torque of the prescribed stress data as the end conditions for an Euler-Bernoulli type beam theory. The practice has been carried over unjustifiably to stress edge conditions for plates and shells (for which the conditions of Saint-Venant's conjecture are not met) while no analogous principles exist for displacement and mixed edge conditions. This volume provides resolutions of these long-standing issues that constitute the foundations of (plate and) shell theories. The book also offers a complete exposition of the static-geometric duality of plate and shell theories that should be more widely applied to simplify theoretical analyses and practical applications. Duality between different classes of physical problems established in this volume makes it possible to avoid solving anew the dual problem of any application.
