Smearing technique for vibration analysis of simply supported cross-stiffened and doubly curved thin rectangular shells

Plates stiffened with ribs can be modeled as equivalent homogeneous isotropic or orthotropic plates. Modeling such an equivalent smeared plate numerically, say, with the finite element method requires far less computer resources than modeling the complete stiffened plate. This may be important when a number of stiffened plates are combined in a complicated assembly composed of many plate panels. However, whereas the equivalent smeared plate technique is well established and recently improved for flat panels, there is no similar established technique for doubly curved stiffened shells. In this paper the improved smeared plate technique is combined with the equation of motion for a doubly curved thin rectangular shell, and a solution is offered for using the smearing technique for stiffened shell structures. The developed prediction technique is validated by comparing natural frequencies and mode shapes as well as forced responses from simulations based on the smeared theory with results from experiments with a doubly curved cross-stiffened shell. Moreover, natural frequencies of cross-stiffened panels determined by finite element simulations that include the exact cross-sectional geometries of panels with cross-stiffeners are compared with predictions based on the smeared theory for a range of different panel curvatures. Good agreement is found.