A singular element based on dual interpolation BFM for V-shaped notches

Abstract

• A new singular element based on dual interpolation boundary face method is proposed. • The new element takes into account the variable singularity orders at the notch tip . • Special basis function is introduced to build the shape functions of the proposed element. • The dual interpolation method can provide much higher accuracy than traditional interpolation method. • The numerical results for stress intensity factors obtained by the new element are convergent. A singular element based on dual interpolation boundary face method (DiBFM) is presented for solving V-shaped notch problems in this paper. The stress field around sharp notches is singular, and the singularity orders vary with the notch angle. Thus an element with usual shape functions or traditional singular element cannot lead to high accurate results. To accurately model the distribution of displacement around the notch tip, a new displacement singular element based on DiBFM is proposed. The new element takes into account the variable singularity orders at the notch tip. The dual interpolation method which combines conventional polynomial element interpolation and moving least-squares approximation can provide much higher accuracy than traditional interpolation method. With the proposed singular element based on DiBFM, more accurate displacement results in the vicinity of the notch tip can be evaluated, thus more accurate stress intensity factor (SIF) of the V-shaped notches can be obtained. Numerical examples have demonstrated the validity and accuracy of our method.