Abstract
The paper first treats the locking problem of shear-elastic plates in bending in the context of multi-grid-methods. A new plate bending element with shape functions of the Allman-type is presented and used for linear and non-linear problems. An important issue is the presentation of a flexible mesh generator with different refinement strategies according to a priori criteria. Different a posteriori criteria for adaptive approximations are given, such as a gradient-based error with one and two indicators for geometrically non-linear load paths, the first being residuum based and the second controlling the geometrical nonlinearities. Branch switching and post-buckling deformation processes are investigated adaptively using these indicators and demonstrated with examples. Another important topic is the automatic dimensional adaptivity of beams and plates within disturbed zones as boundary layers, concentrated load areas and sharp changes of thicknesses This d-adaptivity is combined with h-adaptivity and illustrated by some examples.
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