Transient analysis of tube rolling processes by a semi‐analytical formulation

Published in ''Int. J. Numer. Meth. Engng.'' Vol. 37 (21), pp. 3621-3632, 1994<br />
doi: 10.1002/nme.1620372104
== Abstract ==

A semi‐analytical formulation is presented for transient metal‐forming processes which, being axisymmetric in geometry, are subjected to non‐axisymmetric loads and boundary conditions. The problems are described in terms of the flow formulation, and the pseudo‐concentration method (two material based) is used to account for time integration and non‐axisymmetric free surfaces. Proper Fourier series expansion of both the scalar fields defined to identify the free surfaces and of all the variables of the mechanical problem allows the performance of an advective transport–corresponding to time integration–for a non‐axisymmetric velocity field. A block diagonal matrix is obtained for each harmonic component, as it has been achieved for the constant time solution. The new configuration found as a result of this analysis is taken to calculate the velocity field for the incremented time, which in turn is used to perform the following time step.