A stabilized discrete shear gap extended finite element for the analysis of cracked Reissner–Mindlin plate vibration problems involving distorted meshes

In this work, a new approach in the framework of the local partition of unity finite element method (XFEM) to significantly improve the accuracy of natural frequency in free vibration analysis of cracked Reissner–Mindlin plates is presented. Different from previous approaches, the present formulation is expected to be more accurate and effective in modeling cracked plates by integrating the stabilized discrete shear gap (DSG) into the XFEM setting. Intensive numerical results at low frequency demonstrated that the novel DSG-based XFEM approach possesses the following desirable properties: (1) the awkwardness of transverse shear-locking phenomenon can be overcome easily; (2) the DSG-based XFEM can be applicable to both moderately thick and thin plates straightforwardly; (3) the representation of cracks is independent of finite element mesh; (4) mesh distortion is insensitive and controllable; (5) the accuracy of natural frequency obtained by the present method is high and (6) the present method uses three-node triangular elements that can be much easily generated automatically for problems even with complicated geometry. These properties of the DSG-based XFEM are confirmed through several numerical examples of cracked plates with different boundary conditions.

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