On constructing kinematically admissible velocity fields in cold sheet rolling

The main objective of the presented study is to introduce a rigorous, systematic method for constructing kinematically admissible velocity fields, which are necessary in the analysis of the plastic forming processes by the upper bound method. The mathematical structure of the method is discussed in full detail. To demonstrate the application of the presented method, three different deformation models for the symmetric strip rolling are obtained. And also, to prove the superb accuracy of the deformation models obtained by the presented method, an upper bound solution for the deformation model subjected to the elliptic flow lines family is given. The results obtained in this analysis are compared with the results of modelling in [B. Avitzur, Metal Forming: Processes and Analysis, McGraw-Hill, New York, 1968], and the advantages provided by the presented method, and some new research directions are pointed out.