A reappraisal of transition elements in linear elastic fracture mechanics

摘要

This article offers a detailed comparison of the transition elements described by P.P. Lynn and A.R. In-graffea (International Journal for Numerical Methods in Engineering 12, 103 l-1036) and C. Manu (Engineering Fracture Mechanics 24, 509-512). The source of a numerical phenomenon in using Manu's transition element (TE) is explained. The effect of eight-noded TEs with different quarter-point elements (QPE) on the calculated stress intensity factors (SIFs) is investigated. Strain at the crack tip is shown to be singular for any ray emanating from the crack tip within an eight-noded TE, but strain has both r -1/2 and r1 singularities, with r - 1/2 dominating for large TEs. Semi-transition elements (STEs) are defined and shown to have a marginal effect on the calculated SIFs. Nine-noded transition elements are formulated whose strain singularity is shown to be the same as that of eight-noded TEs. Then the effect of eight-noded and nine-noded TEs with collapsed triangular QPEs, and rectangular and nonrectangular quadrilateral eight-noded and nine-noded QPEs, is studied, and nine-noded TEs are shown to behave exactly like eight-noded TEs with rectangular eight-noded and nine-noded QPEs and to behave almost the same with other QPEs. The layered transition elements proposed by V. Murti and S.Valliapan (Engineering Fracture Mechanics 25, 237-258) are formulated correctly. The effect of layered transition elements is shown by two numerical examples