Numerical analysis of three-dimensional extrusion of elliptic sections by the method of weighted residuals

Abstract

A method of numerical analysis based on the method of weighted residuals is proposed to determine the stresses and strains in three-dimensional extrusion of elliptic sections. In the proposed method, two flow functions and three stress functions are appropriately assumed for the three-dimensional plastic flow. The errors defined for the governing equations and boundary conditions are minimized by introducing the method of weighted residuals in the solution procedure. The work-hardening effect is considered by integrating the effective strain rate following a streamline to a spatially fixed point. Experiments are carried out for an aluminum alloy at room temperature. The computed results are compared with the experimental results as well as with those by the finite element method. The theoretical predictions by the present method in both extrusion load and deformation patterns are in excellent agreement with the experimental results and with those by the finite element method.