ENRICHMENT OF FINITE ELEMENTS WITH NUMERICAL SOLUTIONS FOR SINGULAR STRESS FIELDS

Enriched 2-D and 3-D Þnite elements are formulated for analysis of solids having multi-material junction and wedge conÞgurations that create singular stress Þelds due to the material and/or geometric discontinuities. The order and angular variation of the displacements associated with the singular Þelds are determined from a separate special Þnite element eigenanalysis and used in the enrichment process. The use of these numerically determined singular Þelds allows enriched elements to be developed for complex conÞgurations for which analytical Þelds are not available. In addition to this added ßexibility of application, the current formulation applies to elements that may or may not be in direct contact with the singular point. This allows multiple layers of enriched elements to be used around the singular point and traditional mesh reÞnement studies to be carried out in the enriched element region. Previous enriched formulations have not provided this important capability. For cases where analytical Þelds are available, such as cracked solids, the performance of elements developed with the current approach is shown to be equivalent to that obtained using analytically enriched elements. Mesh reÞnement techniques using enriched elements are described that allow accurate stress distributions and generalized stress intensity factors to be directly determined. The importance of high-order numerical integration, use of multiple layers of enriched elements, and proper choice of the size of the enriched region are demonstrated by comparison to existing solutions for solids with cracks. Application of enriched element modelling to a 2-D bi-material wedge and a 3-D stepped-thickness anisotropic composite laminate is demonstrated