Three-dimensional bending and free vibration analyses of laminated cylindrical panel with/without elastic foundation using two-dimensional discrete method

Abstract

In this paper, a novel isogeometric scaled boundary finite element method (IGSBFEM) is developed to provide a comprehensive investigation into bending and free vibration of laminated cylindrical panels resting on Pasternak foundation. The significant novelty of this method lies in that the proposed formulation is derived based on the three-dimensional (3D) theory of elasticity, while only two-dimensional (2D) reference surface associated with the curvilinear coordinate system needs to be discretized by using isogeometric elements constructed with the non-uniform rational B-splines (NURBS) basis functions, which allows to reduce the computation cost and maintain the exact geometry of problem with desired precision flexibly. The SBFEM governing equation of each single lamina is reduced to a matrix form of first-order ordinary differential equations by introducing a vector of dual variables made of nodal displacements and forces, and the solution can be expressed analytically in terms of the radial coordinate. Therefore, shear locking phenomenon can be overcome naturally without any shear correction factors or reduced integration. The global solving equations of laminated cylindrical panels resting on Pasternak foundation are assembled with a layer-wise method. In addition, the high-order continuous features of isogeometric elements are insensitive to distorted mesh. Therefore, it is compatible with the research of complex geometrical structures with holes. The superior performances of the current approach are testified in the analyses of cylindrical panels with or without elastic foundation, solutions obtained by many other researchers are used for comparison purpose, and effects of several parameters including length and thickness, fiber orientation, stacking sequence and foundation stiffnesses coefficient on the bending or free vibration characteristics are also discussed.