On quadrature and singular finite elements | Zendy

Solecki J. S. | Zendy; Swedlow J. L. | Zendy

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On quadrature and singular finite elements

Author(s) -

Solecki J. S.,

Swedlow J. L.

Publication year - 1984

Publication title -

international journal for numerical methods in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.421

H-Index - 168

eISSN - 1097-0207

pISSN - 0029-5981

DOI - 10.1002/nme.1620200302

Subject(s) - gauss–kronrod quadrature formula , clenshaw–curtis quadrature , tanh sinh quadrature , quadrature (astronomy) , mathematics , gauss–jacobi quadrature , gauss–laguerre quadrature , singularity , mathematical analysis , gauss–hermite quadrature , gaussian quadrature , finite element method , numerical integration , physics , engineering , structural engineering , integral equation , nyström method , optics

Special quadrature rules are described for elastic finite elements that have r q behaviour (0 < q < 1) directly induced in natural element co‐ordinates. In general, the quadrature points and weights can vary with the exponent q. For two‐dimensional problems with a square‐root singularity ( q = 1/2), the use of special quadrature results in significant improvements over regular Gauss quadrature. The development of special quadrature rules for three‐dimensional elements is shown to be a difficult task. Several special case rules are developed and tested for a line‐type singular element, and a precise rule is given for a point‐type singular element in three dimensions.

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