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Enriched finite elements for regions with multiple, interacting singular fields

1996; American Institute of Aeronautics and Astronautics; Volume: 34; Issue: 9 Linguagem: Inglês

10.2514/3.13327

1533-385X

Stephane S. Pageau, Sherrill B. Diggers,

Mechanical stress and fatigue analysis

Enriched two-dimensional finite elements are formulated for analysis of solids with interacting singular points. These elements contain both the order and the angular variation of all singular stress fields emanating from each singular point so that the possible interaction of stress states present in such regions is represented. The order and distribution of the singular fields are determined with a separate finite element eigenanalysis. These field characterizations and the subsequent enrichment are carried out numerically rather than analytically for ease of extension of the technique to complex geometries for which analytical solutions would be difficult to obtain. Generalized stress intensity factors as well as the stresses and displacements result directly from models incorporating enriched elements. Enriched-element models can be applied not only to crack problems but also to singular stress states not involving cracks and crack growth, and are thus more versatile than J-integral and virtual crack-closure techniques used for calculating energy release rates. In addition, the proper angular distribution of the displacement fields leading to each singular stress state is used in formulating the element, an advantage not shared by formulations such as the quarter-point elements. The advantages of using enriched elements containing information from interacting singular points are demonstrated with an example having two interacting singular points. This tensile groove specimen is modeled using these new elements as well as enriched elements that do not take interaction into consideration. Attention is given to modeling issues when using interactive enriched elements.