Dynamic analyses of functionally graded plates with curvilinear stiffeners and cutouts

An isogeometric analysis is used to simulate the vibration and buckling problems of functionally graded plates with curvilinear stiffeners and cutouts. The polynomial splines over a hierarchical T-mesh (PHT-splines) inherit the advantages of nonuniform rational B splines, such as capturing exact geometry, making the flexibility of refinement, reducing computational cost, and getting a higher calculation accuracy. Besides, the PHT splines overcome some drawbacks of the nonuniform rational B splines and make local refinement and free gap representation come true. Thus, using the PHT splines as the base of the isogeometric analysis, the local refinements near the cutouts and the connection areas between the stiffeners and plates are realized. The convergence and correctness of the method are verified by numerical examples. The influences of boundary conditions, the cutout radius, the plate thickness, the plate volume fraction exponent, and the stiffener cross-sectional size on the natural frequencies and buckling loads are also studied. The results show that the degradation of the vibration and buckling performances caused by defects in functionally graded plates can be avoided by adding appropriate stiffeners. Thus, certain vibration and buckling characteristics can be gained by changing the shape and size of the cutouts and stiffeners with no weight growth or even weight deterioration.