Iterative Procedures for Elastic, Plastic and Creep Deformation of Beams

Abstract

Since an analytical solution is not often possible, the determination of deformations in parts subjected to elastic, plastic, thermal and creep strains generally must be obtained by an iterative procedure which requires the aid of a computer. A number of iterative procedures can be used. In view of the fact that the particular procedure adopted may determine whether or not an answer is obtained, some practical methods of solution and their limitations are discussed in detail. The example chosen as a basis for comparison of the various methods is a composite beam subjected to combined bending and axial loads, since this case is reasonably general in that all the strains mentioned above must be considered. Essentially the problem is one of preventing divergence during the solution procedure while at the same time achieving convergence in a reasonable number of iterations. No one method was found that would achieve convergence in all instances. However, a systematic procedure, involving three main methods, termed the strain-bound, Taylor expansion, and averaging methods, is described which enhances the chances of attaining convergence.