Elastoplastic torsion by quadratic programming

A finite element scheme (together with a conjugate gradient algorithm) is demonstrated to be a very effective method for analyzing general elastoplastic torsion of prismatic bars posed as quadratic programming problems. Solutions for bars with elliptical and Sokolovsky's oval cross-sections are presented. The solutions for the elliptical bars agree with the existing elastic and limit plastic solutions at the two extremes of the elastic-plastic range. The algorithm also reproduces accurately the Sokolovsky solution and extends it beyond its limitations.