Vibration and buckling analysis of curvilinearly stiffened plates using finite element method

A finite element method based approach is developed for studying the static, vibration, and buckling behaviors of curvilinearly stiffened plates in the presence of in-plane compressive and tensile stresses. The first-order shear deformation theory 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 remeshed while the stiffener configuration is changed; another advantage is that the results obtained by the present method with a much fewer number of elements match well with the results obtained by using a commercial finite element method 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, inplane load condition, stiffener-plate cross-section area ratio, and stiffness ratio on the static and dynamic behaviors of a curvilinearly stiffened plate are investigated. Results have shown that the 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.