Buckling and Vibration Analysis of Curvilinearly Stiffened Plates with Holes

Additive manufacturing technologies make it possible to stiffen structures in the presence of holes or damage by using arbitrarily shaped stiffeners. To study both the stability and vibration responses of such structural designs, this paper presents an efficient approach in finite element bucking and vibration analysis of a curvilinearly stiffened plate with a hole in the inner zone. A first-order shear-deformable theory is employed for modeling the deflections for both the panel and the curved stiffeners. Displacement compatibility conditions are imposed at the panel-stiffener interfaces. The open source mesh generating tool, DistMesh, is modified to generate 6-noded triangular elements for the plate. Linear strain triangular (LST) elements are used to approximate the domain of the plate with holes. The displacement and geometry of the nodes that constitute the stiffener beam elements are expressed by those of the nodes of the shell elements for the plate through the approximate displacement comparability conditions. The convergence and validation studies related to the buckling and free vibration responses of the curvilinearly stiffened, isotropic panels are conducted. Bucking load and free vibration mode results calculated from the present method are compared against those from the existing literature, and using commercially analysis software, NASTRAN and ABAQUS. The influence of the stiffener shape and the size of the hole on both the plate's vibration and buckling responses is extensively studied. Parametric studies show that curvilinear stiffeners can increase the free vibration fundamental frequency and the bucking load of the damaged plate to a larger value than that of the stiffened plate with straight stiffeners.