Study on the theory and application of the energy method for analyzing compressive instability in sheet forming

It is pointed out that there was serious weakness when using the energy method for studying compressive plastic instability in sheet forming in the past. When applying the deduced instability strengths to relative engineering analysis, theoretical solutions departed from practices. The basic reason is that the simplified process in mathematical analysis of elastic bending energy was completely applied to that of plastic bending energy. Whilst the camber expressed by a function of the displacement normal to a plate was approximated to realistic deflective camber, the displacement of the deflected plate in the compressed direction was neglected. With the aid of improved instability strengths, the predictions on both the critical buckling dimension of the blank in cup deep-drawing without a blankholder through a cylindrical or a conical die with the minimum blankholder pressure to prevent buckling under constant load are universally in agreement with both experimental results and experiential data. The general equations for the energy and the work done by internal force in the plastic bending of a plate are given in this paper. With the aid of the method proposed by the author, they maybe used for analyzing the plastic buckling of a shell with a bending moment.