NURBS-based isogeometric analysis of laminated composite beams using refined sinus model

An isogeometric formulation based on non-uniform rational B-spline (NURBS) basis functions is presented for the analysis of laminated composite beams. A refined sinus model is considered in deriving the governing equations using the principle of virtual work. This refined sinus model does not require shear correction factor and ensures continuity conditions for displacements, transverse shear stresses as well as boundary conditions on the upper and lower surfaces of the laminated beam. It is important to notice that the number of the mechanical unknowns is independent of the number of layers. The proposed isogeometric finite element does not suffer from shear locking. Both static and vibration mechanical tests for thin and thick laminate beams are presented in order to validate the capability of the proposed isogeometric formulation. For different boundary conditions, fiber orientations and lay-up number, excellent agreement is found between the results obtained from the present formulation and reference results from open literature or finite element reference solutions.