Metal Forming Analysis by Fourier Series Expansion and Further Uses of Pseudo-Concentrations

Abstract

An analysis of metal forming processes with axial geometry is performed by an expansion in Fourier Series on the circunferential direction. For that purpose, an incremental form is presented on the basis of the flow formulation. For every increment of the non-null imposed boundary conditions an algebraic system is formed in which the non-linearity due to the visco-plastic properties of the material is placed as part of the load term. In this way, the global stiffness matrix is block diagonal, the coupling due to material non-linearity being included in the right hand side. Free surfaces are treated as an interface inside the elements, as an extension of the pseudo-concentration method.