A Group of Isoparametric Elements Suitable for St.Venant's Torsion of a Bar with Cracks

In this paper,we shall give a group of new isoparametric elements suitable.for St.Wenant's torsion of a bar with vertical cracks.These elements are eight-point isoparametric element,quarter eight-Point isoparametric element and eight-point isoparametric transition element.Among these elements,the second and the third elements 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 radial vertical crack.The calculated results show that the isoparametric elements given bythis paper have ideal accuracy,good convergence.high speed of convergence,low freedom and little computational time,and so they can be widely applied to practice.