On SBFEM analysis of complex stiffened cylindrical shells with combined shell-curved beam element: Static and free vibration

Abstract

In this paper, a novel semi-analytical numerical model based on the scaled boundary finite element method (SBFEM) is developed for the static and free vibration analyses of the stiffened cylindrical shells. The SBFEM is a numerical technique in which only the surfaces or boundaries of the computational domain need to be discretized, while an analytical formulation can be derived in the radial direction of the surrounding area. These advanced features enable the spatial dimension to be reduced by one, while the accuracy of the proposed algorithm is maintained. The stiffened shell structure is divided into the shell and stiffeners (curved beam and straight beam), and the basic physical equations as well as the associated boundary conditions of each part are described according to the elasticity theory. The surface of shell and the axis of stiffener are discretized, then the ordinary differential governing equations of shell and stiffeners are derived in the scaled boundary coordinate system using the virtual work principle. Based on the continuity conditions of displacement, the shell and stiffeners are assembled together, and the coupling stiffness and mass matrices are derived. Furthermore, the semi-analytical solutions are obtained by using Padé series expansion method, and the natural frequencies of the stiffened shell are determined through generalized eigenvalue analysis. Comparisons between the present numerical results and solutions available in the published work have been carried out to demonstrate the convergence and accuracy of this approach. At the same time, the influences of the geometric parameters and stiffener configuration on the static and free vibration behaviors of the stiffened cylindrical shells are studied in detail.