Abstract: In this paper, we shall give a group of new isoparametric elements suitable.for St.Wnant’s torsion of a bar with vertical cracks. These elements are eight-pointisoparametric element, quarter eight-Point isoparametric element and eight-pointisoparametric transition element. Among these elements, the second and the thirdelements possess the singularity of order r^-1/2 at crack tip. Using these elements, wehave completed the calculations of St. Venant’s torsion for a cylinder with a radialvertical crack. The calculated results show that the isoparametric elements given bythis paper have ideal accuracy. good convergence. high speed of convergence, lowfreedom and little computational time, and so they can be widely applied to practice.

Key words: singular finite element, transition finite element, fracturemechanics, St, Venant’s torsion