Ss. Pageau et Sb. Biggers, ENRICHMENT OF FINITE-ELEMENTS WITH NUMERICAL-SOLUTIONS FOR SINGULAR STRESS-FIELDS, International journal for numerical methods in engineering, 40(14), 1997, pp. 2693-2713
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.