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

Sundararajan Natarajan, Stéphane P A Bordas, D. Roy Mahapatra

Research output: Chapter in Book/Conference paperConference paper

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationIUTAM Symposium on Multi-Functional Material Structures and Systems - Proceedings of the IUTAM Symposium on Multi-Functional Material Structures and Systems
Pages297-304
Number of pages8
Volume19
DOIs
Publication statusPublished - 2010
Externally publishedYes
EventIUTAM Symposium on Multi-Functional Material Structures and Systems - Benguluru, India
Duration: 10 Dec 200812 Dec 2008

Publication series

NameIUTAM Bookseries
Volume19
ISSN (Print)18753507

Conference

ConferenceIUTAM Symposium on Multi-Functional Material Structures and Systems
CountryIndia
CityBenguluru
Period10/12/0812/12/08

    Fingerprint

Cite this

Natarajan, S., Bordas, S. P. A., & Mahapatra, D. R. (2010). On numerical integration of discontinuous approximations in partition of unity finite elements. In IUTAM Symposium on Multi-Functional Material Structures and Systems - Proceedings of the IUTAM Symposium on Multi-Functional Material Structures and Systems (Vol. 19, pp. 297-304). (IUTAM Bookseries; Vol. 19). https://doi.org/10.1007/978-90-481-3771-8-30