Finite Element Methods for Thin Shell Problems

Finite Element Methods for Thin Shell Problems Michel Bernadou Pôle Universitaire Léonard de Vinci, Paris La Défense, and INRIA-Rocquencourt, France This self-contained book provides a complete mathematical analysis of general thin shell equations and gives a representative set of numerical analysis results on thin shell problems by emphasizing their approximation and implementation. The main results of mathematical and numerical analysis related to the approximation of the solutions of thin shell problems by various finite element methods are presented. The different classical models of thin shells are considered, the existence and the uniqueness of solutions as well as the convergence of the different methods are studied. Beyond this theoretical analysis, the implementation and the use of these various finite element methods to solve engineering problems, such as arch dams, turbine blades, shell junctions, buckling loads and shape optimization, are carefully described.