Adaptive mesh refinement for localised phenomena

Abstract

The present work is concerned with the development, testing and use of finite element based methods in conjunction with adaptive mesh refinement procedures for the solution of three types of static and dynamic stress analysis problems. First, an adaptive mesh refinement procedure is introduced and used in static plate bending finite element analysis based on Mindlin-Reissner assumptions to study the edge effects which occur in plates with certain types of boundary conditions. Several issues of finite element mesh dependence and adaptivity in strain localisation problems are then discussed and illustrated. Finally, adaptive finite element methods for the solution of two-dimensional transient dynamic stress analysis problems are developed and tested on some benchmark examples. In all cases cited above there is a need to refine the finite element mesh locally in certain zones either within or at the boundary of the domain under consideration. In the transient dynamic analysis there is a further problem; these zones will move with time.