In this paper, a domain integral method to evaluate the J-integral along with a singular patch method for three-dimensional linear elastic fracture mechanics analyses using Isogeometric analysis (IGA) are presented. The analyses are carried out using a singular patch method that can realize the square-root singularity in the stress distribution in the vicinity of the crack front. The sizes of IGA elements adjacent to the crack front are generally much larger than those of finite elements in the crack analysis. The proposed domain integral method enables a pointwise evaluation of the J-integral at a point on the crack front curve. To achieve it, integral domain with a very small thickness is set at the crack front. To examine the accuracy, the proposed methods are applied to the problems of semi-elliptical crack problems with high aspect ratios. Stress intensity factors are computed by the J-integral method. The proposed methods are found to evaluate the stress intensity factors accurately.

The singular patch method for isogeometric analysis (IGA) to represent the singular stress behavior in the vicinity of a crack tip for two-dimensional linear elastic fracture mechanics analysis is presented. The singular stress behavior can be realized by appropriately placing the control points in the finite element method. This paper describes the general procedure to choose their positions when the quadratic B-spline functions are used for the IGA discretization. The accuracy of the proposed singular patch method is critically examined through evaluated stress intensity factors (SIFs) by the J-integral method and stress distributions in the vicinity of the crack tip. The results of the computations using the singular patch method are found to be very accurate.

No abstract

No abstract