Recent Developments in Anisotropic Heterogeneous Shell Theory

This book presents approaches to numerical-analytical solutions of problems in the mechanics of shells with various structures and shapes based on refined and spatial models. It examines the mechanical behavior of shallow, circular and noncircular, conical, spherical, and functionally graded shells obtained by the refined model. Solving problems in shell theory involves the use of various numerical methods and can entail considerable computational difficulties. The approach is built on reducing the original partial system to systems of ordinary differential equations with the help of spline approximations, which are then solved using the discrete-orthogonalization method. Studying these problems results in severe computational difficulties, since partial differential equations with variable coefficients constitute the original model.§§The book investigates the stress-strain state and free vibrations of finite-length cylinders in spatial formulation (3D elasticity theory). Further, it analyzes the influence of geometrical and mechanical parameters, of boundary conditions, and of the loading character on the distributions of stress and displacement fields and on the dynamical characteristics in these shells and cylinders. Lastly, it discusses in detail the validation of the reliability of the results obtained by numerical calculations.§