Computational Aspects of Adaptive Dimensional Reduction for Nonlinear BoundaryValue Problems

摘要

There has been increased interest recently in feed-back methods for reliable,robust, efficient computational methods in mechanics. We will outline the construction of such methods for a class of problems describing special (anti-plane shear) deformations of bars of rectangular or arched cross section. In particular, we will show how to reduce the dimension of the underlying problem adaptively . For brittle or linear materials, this method is adaptive (optimal in rate of convergence). We shall emphasize the computational aspects tht have practical import to the performance of this method, such as the construction of a posteriori error estimators that are simple to compute, the selection of basis functions in the dimensional reduction and the heuristic principle for extension. We will illustrate these concepts with computations. (JHD)