The effect of varying thickness on the buckling of orthotropic plates

Although stability failure of constant thickness plates is a fairly well understood problem, buckling of plates with varying thickness has seen little research. This is not a common problem, but buckling of varying thickness plates does occur, as in the case of Advanced Grid Stiffened structures. These structures are characterized by lattices of rigidly connected rib stiffeners. While real-world Advanced Grid Stiffened structure ribs are modeled as orthotropic plates, they often have complex cross-sections (i.e., varying thickness). Unfortunately, failure analysis techniques for these ribs have been limited to rectangular cross-sections. To address this shortcoming, a buckling theory is presented for orthotropic plates of varying thickness. Orthotropic plates with both linear and hourglass thickness variations are considered. These are common grid structure cross-section geometries resulting from existing manufacturing processes. For both geometries, results are given that allow designers to predict how these plates will behave, relative to a constant thickness plate, for a variety of material properties and plate aspect ratios.