Thermo-Dynamics of Plates and Shells

This monograph is devoted to the investigation of nonlinear dynamics of plates and shells embedded in a temperature field. Numerical approaches and rigorous mathematical proofs of solution existence in certain classes of differential equations with various dimensions are applied. Both closed shell-type constructions and sectorial shells are studied.§The considered problems are approximated by 2D and 3D constructions taking into account various types of nonlinearities (geometrical and/or physical with coupled deformation and temperature fields), and are subjected to an action of stationary and non-stationary thermal loads.§Variational and finite difference numerical approaches are used to study numerous problems important for civil and mechanical engineering.§Furthermore, a novel and exact computational method to solve large systems of linear algebraic equations especially suitable for computational speed and memory storage of a computer is proposed.§This book is expected to be useful for researchers, engineers and students dealing with thermal and dynamical problems of stability and strength of shell-type constructions. This monograph is devoted to nonlinear dynamics of thin plates and shells with thermosensitive excitation. Because of the variety of sizes and types of mathematical models in current use, there is no prospect of solving them analytically. However, the book emphasizes a rigorous mathematical treatment of the obtained differential equations, since it helps efficiently in further developing of various suitable numerical algorithms to solve the stated problems.