Free vibration analysis of isogeometric curvilinearly stiffened shells

The isogeometric analysis (IGA) proposed by Hughes is a new approach in which Non-Uniform Rational B-Splines (NURBS) are used as a geometric representation of an object. It has superiorities of capturing exact geometry, simplifying refinement strategy, easily achieving degree elevation with an arbitrary continuity of basic functions and getting higher calculation accuracy. In this paper, the IGA approach is extended to solve the free vibration problem of curvilinearly stiffened cylindrical and shallow shells. The first-order shear deformation theory (FSDT) and the Reissner-Mindlin shell theory are used to model the shells, and the three-dimensional curved beam theory is employed to model the stiffener which can be placed anywhere within the shell. Some numerical examples are solved to study the vibration behavior of the curvilinearly stiffened shells. The effects of shell and stiffener element numbers, boundary conditions, stiffener ply modes and shell thicknesses on the natural frequency are investigated. Results have shown the correctness and superiorities of the present method by comparing the results with those from commercial finite element software and some numerical methods in existing literatures. One of the advantages is that the element number is much less than commercial finite element software, whereas another is that the mesh refinement process is much more convenient compared with traditional finite element method (FEM).