Buckling and vibration of stiffened panels or single plates with clamped ends

An efficient method for the buckling and vibration analysis of plates or stiffened panels with clamped ends is presented. The method uses Lagrangian multipliers to couple sinusoidal modes with appropriate half-wavelengths of response, thereby enforcing the end conditions at discrete point supports. Clamped ends can usually be modelled accurately using only a few point supports, while arguments from symmetry often enable some of the required end conditions to be satisfied without explicitly applying constraints. In such cases few half-wavelengths are needed to obtain excellent accuracy. Solutions obtained for the simple limiting case of single plates are exact or within 1% of the classical or other reported solutions. Solutions obtained for stiffened panels are in close agreement with those obtained using finite element analysis.