Minimum weight bars for given lower bounds on Euler buckling load and frequency of longitudinal vibration (Q1090162)

The necessary optimality conditions are developed for the problem of minimizing the mass of a structural member subject to design constraints on two fundamental eigenvalues, namely frequency of longitudinal vibration and Euler buckling load. The regions of the design space, in which each of the constraints is active, are delineated. An effective numerical solution procedure is derived and solutions are obtained for a wide range of the design variables for beams of both solid cross-section and sandwich construction. The optimal designs are compared with a prismatic beam satisfying the design constraints.