The Methods of Ritz, Galerkin, and Complementary Energy Applied to Some Nonconservative Problems of Elastic Stability

摘要

The well-known problem of Beck and two problems due to Hauger which arise in the theory of nonconservative elastic stability are reconsidered. Approximate values of the respective critical loads are computed by means of the methods of Ritz, Galerkin, and complementary energy in conjunction with a formal variational expression and the adjoint variational principle. For these examples, it was found that the speed of convergence of the procedures is somewhat better in the case of the method of complementary energy, but the Galerkin procedure is probably the simplest to apply. The numerical calculations demonstrate that the previously published values of the critical load intensity for Hauger's two problems are about 5% and 28% too high. (Author)