Finite element approach to the static, vibration and buckling analysisof curvilinearly stiffened plates

A finite element method based approach is developed for studying the static, vibration and buckling behavior of curvilinearly stiffened plates in the presence of in-plane compressive and tensile stresses. The first order shear deformation theory (FSDT) is employed for both the plate and the Timoshenko beam modeling. Interpolation functions are used to build the displacement mapping between the stiffener and the plate nodes to allow the stiffener to be placed anywhere within the plate. One of the advantages of the present method is that the plate need not be re-meshed while the stiffener configuration is changed, and second, results obtained by the present method with much fewer number of elements match well with the results obtained by using a commercial FEM software. Several numerical examples are solved to study both the static and dynamic behaviors of stiffened plates. The effects of boundary conditions, stiffener eccentricity, stiffener curvature, stiffener-plate geometry parameters, in-plane load condition, stiffener-plate cross-section area ratio and stiffness ratio on the static and dynamic behaviors of curvilinearly stiffened plate are investigated. Results have shown that behavior of the natural frequency parameter as a function of applied in-plane stress could be affected by the plate thickness, in-plane load condition, stiffener-plate cross-section area ratio and stiffness ratio during compression only, but not when subjected to in-plane tension.