Reference : On numerical integration of discontinuous approximations in partition of unity finite...
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On numerical integration of discontinuous approximations in partition of unity finite elements
Natarajan, S. [Theoretical, Applied and Computational Mechanics, Cardiff School of Engineering, Cardiff, United Kingdom]
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Mahapatra, D. R. [Department of Aerospace Engineering, Indian Institute of Science, Benguluru 560012, India]
IUTAM Bookseries
IUTAM Symposium on Multi-Functional Material Structures and Systems
10 December 2008 through 12 December 2008
[en] Composites ; Discontinuous enrichment ; GFEM ; Material interfaces ; Numerical integration ; Open source MATLAB code ; Schwarz-Christoffel conformal mapping ; Singularity ; Strain smoothing ; XFEM ; Matlab code ; Numerical integrations ; Composite materials ; Conformal mapping ; Finite element method ; Fracture mechanics ; Functional materials ; Geometry ; Integration ; MATLAB ; Interfaces (materials)
[en] 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. © 2010 Springer Science+Business Media B.V.
International Union of Theoretical and Applied Mechanics (IUTAM)
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