Fundamentals of Discretization Methods

This chapter gives a concise introduction into modern discretization concepts that are used for the stress analysis of structures and in fluid–structure interaction problems. Departing from a by now classical concept, namely the finite element method, mesh-free methods and partition-of-unity-based discretization methods are introduced. Since the majority of the structural applications in aerospace engineering concern thin-walled structures, some attention is given to shell elements. In view of the rapidly increasing use of laminated composites, interface elements are also briefly treated. Furthermore, the growing importance of multiscale analysis as a new paradigm is discussed. Keywords: finite element methods; mesh-free methods; multiscale methods; nonlinear analysis; shell elements; interface elements