Vibration of Plate with Curvilinear Stiffeners Using Mesh-Free Method

The element-free Galerkin method, which is based on the moving-least-squares approximation, is developed for vibration analysis of unitized structures (e.g., a plate with curvilinear stiffeners). The plate and stiffeners are modeled using the first-order shear deformation theory and Timoshenko beam theory, respectively. The moving-least-squares approximation does not satisfy the delta function property. Consequently, an approximation method (e.g., the well-known penalty method) must be used for imposing essential boundary conditions. A key benefit of using element-free Galerkin for the vibration analysis of a stiffened panel is that the locations and curvatures of the stiffeners can be changed without modifying the plate nodes. Numerical results for different stiffeners, configurations, and boundary conditions are presented. All results are verified using the commercial finite-element software ANSYS. Excellent agreement is seen in all cases. A comparison of the present formulations with other available results for stiffened plates is also made. The mesh-free approach yields highly accurate results for the plates with curvilinear stiffeners.