A Study of the Accuracy of the Galerkin Method on the Basis of Exact Buckling Loads of Nonconservatively Loaded Elastic Bars.

It is shown that the differential equation for a nonconservative elastic system of divergence type can be transformed into the differential equation for a bar with a variable moment of inertia subjected to a concentrated conservative end load. Existing exact solutions of the conservative problem can be used to find exact buckling loads of the nonconservative problem. Several examples are given which are also solved approximately by Galerkin's method in order to demonstrate the accuracy of the latter method. It is found that two- or three-term approximations in general yield good agreement with the exact results, although they may also lead to results which are even qualitatively erroneous.