An extended edge-based smoothed discrete shear gap method for free vibration analysis of cracked Reissner–Mindlin plate

Abstract

• An XES-DSG3 element is proposed for free vibration analysis of cracked plates. • The strain gradient matrices with enriched functions are smoothed. • The present method takes advantage of both SFEM and XFEM. • The discrete shear gap method is employed to eliminate the shear-locking. • The computational accuracy of XES-DSG3 is insensitive to mesh distortion. An extended edge-based smoothed discrete shear gap method (XES-DSG3) is proposed for free vibration analysis of cracked Reissner–Mindlin plate by implementing the edge-based strain smoothing operation into the discrete shear gap-based extended finiteelement method (XFEM-DSG3). In present method, the strain smoothing operation is implemented into the bending strain gradient matrices, in which the enriched functions are included. Then, the derivatives of element shape functions and derivatives of crack-tip singular enriched functions are not required in the computation. The calculation of element matrices is performed over the smoothing domains which are associated with edges of elements. The transverse shear locking of Reissner–Mindlin plate can be avoided by using the integration of discrete shear gap (DSG) method. Several numerical examples are investigated to illustrate the accuracy of XES-DSG3 for the free vibration analysis of cracked Reissner–Mindlin plate. Moreover, numerical results show that the present method is insensitive to mesh distortion and it is more stable than the pervious XFEM-DSG3.