Optimum stiffened panel design with fundamental frequency constraint

A generic analysis/design method for prismatic plate assemblies, using exact plate stiffnesses which are transcendental functions of loading and/or vibration frequency, has long been validated by the established program viconopt. Hitherto vibrations were permitted only in analysis because design uses the Wittrick–Williams algorithm to modify the design predicted by a linear optimiser to be ‘just stable’ by scaling all layer thicknesses by F. This works because buckling loads, unlike the fundamental frequency f1, vary monotonically with F. The paper considers additionally scaling all plate breadths by Fα such that the buckling loads and f1 all vary monotonically with F. Theoretical consideration of simple limiting cases establishes bounds on the permitted values of α as 0.1≤α≤0.4. Then viconopt results for typical stiffened panels demonstrate the method to be correct and are used to investigate the value of α which is most effective in returning stabilised designs of least mass and with least computation.