Isogeometric static and dynamic analysis of laminated and sandwich composite plates using nonpolynomial shear deformation theory

An effective numerical approach based on the isogeometric analysis (IGA) employing nonpolynomial shear deformation theory (NPSDT) has been proposed and implemented in the present work for the static and dynamic analysis of laminated and sandwich composite plates. The theory assumes the nonlinear distribution of transverse shear stresses, and also satisfy the zero transverse shear deformation at the top and bottom surfaces of the laminates. Using Hamilton's principle, the governing equation of motion is derived and then discretized based on the IGA technique, which facilitates the use of non-uniform rational B-splines (NURBS) basis functions to easily satisfy the stringent continuity requirement of the NPSDT model (C-1-continuity) without any additional variables. The set of governing equations are solved to obtain transient response using Newmark's time integration scheme. Fourier transformation is carried out on the transient response to obtain the natural frequency. Various numerical examples covering different features of present modeling for laminated and sandwich plates are investigated. The performance of the model has been observed by comparing the evaluated results with different published results available in the open literature which ascertain its precision and range of applicability at a reduced computational cost.