On quadrature and singular finite elements

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Abstract
Special quadrature rules are described for elastic finite elements that haverqbehaviour (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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