Finite Element Analysis of Steady Flow in Metal Processing

A finite element method has been proposed to steady flow problems in metal processing. First assume the stream lines and divide each band between the stream lines into triangular elements . Obtain the stiffness matrix for the problem, introduce the boundmy condition, and obtain the nodal point displacement increment and the strainand stress-increments in the same manner as the non-steady flow problem. The strain and stress of the element are obtained by integrating these increments along the stream line, calculate the nodal point force from the stress, evaluate the validity of the boundary condition, and conect the unsuitable boundary condition if the condition is not satisfied. The solution is obtained by the iterative calculation until the convergence is adequate. Furthermore , the solution of strip rolling such as the skin pass rolling is presented, and the deforming configuration of the strip and the stress distribution are figured out. Although the pr'esent analytical method is aptJlicable to the other steady metal jJrocessings such as drawing and extrusion , the establishment of the analysis method for the case of large reduction is a subject to be studied further.