Free flexural vibration of cracked composite laminated plate using higher-order XFEM

In this work, a higher-order XFEM approach is presented and implemented to analyze free flexural vibration in cracked composite laminated plate using higher-order shear deformation theory. The composite laminated plate experiences flexural vibration during its service life due to transverse shear loading. Out-of-plane modulus of the plate is much lesser than the in-plane modulus, so the free vibration study of the plate has become a crucial parameter for a safe service environment. The proposed methodology introduce higher-order tip enrichment functions (r2 terms) for crack simulation in laminated plate. These enrichment functions efficiently capture all conceivable displacements and rotations near the crack tip region. A comparative analysis between higher-order XFEM and conventional XFEM approach is presented in terms of computational accuracy. Several numerical examples are presented to demonstrate the accuracy of these higher-order enrichment functions, which contain variations in natural frequency with respect to crack sizes for different symmetric ply composite laminate plates under varied boundary conditions. The numerical results demonstrate that the proposed higher-order XFEM approach is significantly enhancing computational accuracy than the classical XFEM approach.