ANALYSIS OF NONLINEAR MODEL PROBLEMS BY THE FINITE ELEMENT METHOD OF LINES—Ⅳ. ELASTIC-PLASTIC TORSIN

As the final paper in this series of nonlinear application of the finite element method of lines (PEMOL), the present paper applies this method to material nonlinear problems by presenting a FEMOL analysis of the elastic-plastic torsion problem. Firstly, the elastic region of the cross-section is discretized by FEMOL elements. Next the changes of nodal lines at end-points on the elatic-plastic interface are taken as shape variables which are incorporated into the ODE system by using the trivial ODE technique with the supplementary BCs provided by the yield condition of a weakform. As a result, the elastic-plastic torsion problem is transformed into a standard nonlinear ODE problem and then solved by standard ODE solvers. Numerical examples are given to show the good performance of the present approach.