Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates

An effective, simple, robust and locking-free plate formulation is proposed to analyze the static bending, buckling, and free vibration of homogeneous and functionally graded plates. The simple first-order shear deformation theory (S-FSDT), which was recently presented in Thai and Choi (2013) [11], is naturally free from shear-locking and captures the physics of the shear-deformation effect present in the original FSDT, whilst also being less computationally expensive due to having fewer unknowns. The S-FSDT requires C1-continuity that is simple to satisfy with the inherent high-order continuity of the non-uniform rational B-spline (NURBS) basis functions, which we use in the framework of isogeometric analysis (IGA). Numerical examples are solved and the results are compared with reference solutions to confirm the accuracy of the proposed method. Furthermore, the effects of boundary conditions, gradient index, and geometric shape on the mechanical response of functionally graded plates are investigated.