Optimal stabilization of indefinite plate buckling problems

Abstract

Indefinite plate buckling problems arise when the applied load case results in buckling loads which are not all of the same sign. Examples include the important cases of shear buckling and general combinations of tensile and compressive in-plane edge loads. Optimal controllers which actively stabilize these general, indefinite plate buckling problems, by transforming them into a system of definite plate buckling problems, are presented. Important features of this approach include the ability to select the designed closed loop critical buckling load, and to pre-determine what load cases a given controller will stabilize when the exact load combination varies or is unknown. This last result enables the control designer to know exactly, by design, what load combinations will be stabilized. A numerical example is presented where the controllers developed are employed to stabilize multiple, definite and indefinite buckling modes for laminated composite plates similar to aircraft wing skins.