Single Domain Quadrature Techniques for Discontinuous and Non-Linear Enrichments in Local Partion of Unity FEM
The problem of the evaluation of the stiffness matrix for finite elements enriched by discontinuous/non-linear functions is investigated. If the introduction of discontinuities inside the elements through enrichment functions is nowadays well established by local partition of unity techniques, the evaluation of the element stiffness requires splitting the element into quadrature subcells where appropriate quadrature rules apply. To overcome this problem a technique is suggested, called polynomial mapping, based on replacing the enrichment function with polynomials having the same integral of the original function. These polynomials are function of the position of the discontinuity and are defined on the entire element domain, therefore avoiding the generation of quadrature subcells. The technique is applied to discontinuities in the displacement and strain and is introduced for regularized jumps in the displacement. An integration error analysis is shown in the latter case.
KeywordsExtended finite element method partition of unity regularized displacement jump quadrature equivalent polynomial.
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