Lower Bounds for the Buckling Loads and the Fundamental Frequencies of Elastic Bodies

Abstract

Within the classical theory of elastic stability a lower bound to the buckling load of an elastic body is presented. The Timoshenko load is shown to be a better upper bound to the buckling load than the Rayleigh load. By appropriate modifications of the potential and complementary energies, these bounds are applicable to the fundamental frequency of an elastic body. The application of the bounds is illustrated.