ENRICHMENT OF FINITE-ELEMENTS WITH NUMERICAL-SOLUTIONS FOR SINGULAR STRESS-FIELDS

Enriched 2-D and 3-D finite elements are formulated for analysis of so lids having multi-material junction and wedge configurations that crea te singular stress fields due to the material and/or geometric discont inuities. The order and angular variation of the displacements associa ted with the singular fields are determined from a separate special fi nite element eigenanalysis and used in the enrichment process. The use of these numerically determined singular fields allows enriched eleme nts to be developed for complex configurations for which analytical fi elds are not available. In addition to this added flexibility of appli cation, the current formulation applies to elements that may or may no t be in direct contact with the singular point. This allows multiple l ayers of enriched elements to be used around the singular point and tr aditional mesh refinement studies to be carried out in the enriched el ement region. Previous enriched formulations have not provided this im portant capability. For cases where analytical fields are available, s uch as cracked solids, the performance of elements developed with the current approach is shown to be equivalent to that obtained using anal ytically enriched elements. Mesh refinement techniques using enriched elements are described that allow accurate stress distributions and ge neralized stress intensity factors to be directly determined. The impo rtance of high-order numerical integration, use of multiple layers of enriched elements, and proper choice of the size of the enriched regio n are demonstrated by comparison to existing solutions for solids with cracks. Application of enriched element modelling to a 2-D bi-materia l wedge and a 3-D stepped-thickness anisotropic composite laminate is demonstrated. (C) 1997 by John Wiley & Sons, Ltd.