NURBS-based isogeometric analysis of buckling and free vibration problems for laminated composites plates with complicated cutouts using a new simple FSDT theory and level set method

We combine the isogeometric analysis, the level set and a simple first-order shear deformation theory (S-FSDT) to form a new effective and accurate approach for simulating free vibration and buckling problems of laminated composite plates with cutouts. The problem domain is discretized using non-uniform rational B-spline (NURBS) basis functions, which are utilized for geometry and field variables approximation. In S-FSDT, the shear locking effect is no longer valid and more interestingly, low computational cost is saved because of having fewer unknowns. The trimmed NURBS surface often used in existing approaches, which has some disadvantages in describing the geometrical structure with internal cutouts due to the tensor product of the NURBS basis functions, is no longer required in the present formulation, and the level set method (LSM) is employed to describe the cutouts instead. More interestingly, the numerical integration in the developed method is performed only inside the physical domain. All those features make the method effective in modeling cutouts with complicated shapes. Numerical examples are presented to show the performance of the method. The results obtained are validated against reference solutions showing a good agreement and performance.