Buckling and vibration extended isogeometric analysis of imperfect graded Reissner-Mindlin plates with internal defects using NURBS and level sets

The critical buckling parameters and natural frequencies of defective functionally graded material (FGM) plates with internal cracks or voids are extracted by using an effective numerical approach, combining the extended isogeometric analysis based on non-uniform rational B-spline (NURBS) and Reissner-Mindlin plate theory. The defects are captured by enrichment while the discontinuities are represented by level sets. The shear locking is treated by multiplying a factor into the shear terms. Numerical examples of imperfect FGM plates demonstrate the accuracy of the present method. Effects of gradient index, discontinuity location, crack-length, width-to-thickness, boundary conditions, etc. on frequencies and buckling coefficients are investigated.