ADAPTIVE FINITE ELEMENT APPROACH TO A PLATE PROBLEM.

A general problem in finite element analysis is the design of optimal FE-meshes, which should be fine enough to produce sufficient accuracy. At the same time too large a number of elements has to be avoided in view of computer time and storage requirements. Therefore an optimal mesh should be graded according to a uniform error distribution. As the error can hardly be predicted by the data, the finite element solution itself should provide some information on the magnitude and distribution of the error. These a-posteriori-estimates have been put on a reliable mathematical foundation for a class of bilinear forms by Babuska et al. in the energy norm. Computer error estimators for the magnitude and error indicators for the distribution of the error have been obtained for some one-dimensional problems and for the problem of plain strain and plane stress. In this paper the general theory of Babuska is applied to plate-problems according to Mindlin's plate theory. In contrast to Kirchoff's theory shear forces are considered. Thus, better results near corners are obtained and, furthermore, thick plates can be treated. For quadrilateral elements an error indicator is derived, which is composed of element residuals and of the jumps of bending moments and shear forces across element edges.