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On numerical integration of discontinuous approximations in partition of unity finite elements

Natarajan, Sundararajan, Bordas, Stephane Pierre Alain ORCID: and Mahapatra, D. Roy 2010. On numerical integration of discontinuous approximations in partition of unity finite elements. Presented at: IUTAM Symposium on Multi-Functional Material Structures and Systems, Bangalore, India, 10-12 December 2008. Published in: Dattaguru, B., Gopalakrishnan, S. and Aatre, V. K. eds. IUTAM Symposium on Multi-Functional Material Structures and Systems. IUTAM Bookseries (19) Dortrecht: Springer, pp. 297-306. 10.1007/978-90-481-3771-8_30

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This contribution presents two advances in the formulation of discontinuous approximations in finite elements. The first method relies on Schwarz-Christoffel mapping for integration on arbitrary polygonal domains [1]. When an element is split into two subdomains by a piecewise continuous discontinuity, each of these polygonal domains is mapped onto a unit disk on which cubature rules are utilized. This suppresses the need for the usual two-level isoparametric mapping. The second method relies on strain smoothing applied to discontinuous finite element approximations. By writing the strain field as a non-local weighted average of the compatible strain field, integration on the surface of the finite elements is transformed into boundary integration, so that the usual subdivision into integration cells is not required, an isoparametric mapping is not needed and the derivatives of the shape (enrichment) functions do not need to be computed. Results in fracture mechanics and composite materials are presented and both methods are compared in terms of accuracy and simplicity. The interested reader is referred to [1,6,13] for more details and should contact the authors to receive a version of the MATLAB codes used to obtain the results herein.

Item Type: Conference or Workshop Item (Paper)
Date Type: Publication
Status: Published
Schools: Engineering
Uncontrolled Keywords: Composites; Discontinuous enrichment; GFEM; Material interfaces; Numerical integration; Open source MATLAB code; Schwarz-Christoffel conformal mapping; Singularity; Strain smoothing; XFEM
Publisher: Springer
ISBN: 9789048137701
Last Modified: 20 Oct 2022 09:21

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