ANALYSIS OF THE HYDROSTATIC BULGING OF AN ELLIPTIC DIAPHRAGM BY THE ENERGY METHOD

Abstract

An approach using the energy method is proposed for the analysis of three-dimensional sheet-metal forming. There are some limitations in analysis by the energy method, e.g., the analytical expression of the geometric configuration and the construction of a proper kinematically-admissible velocity field are very difficult and the estimation of strain rate at a point on the surface is very complicated. In the method suggested, the principal components of strain increment are calculated directly from the change of geometric profile for an arbitrary triangular element. The corresponding solution is found through optimization of the total energy consumption with respect to some parameters assumed in the kinematically-admissible velocity field and the geometric profile. In order to check the validity of the method proposed, the hydrostatic bulging of an elliptic diaphragm has been analyzed. In comparison of the computed results with existing experimental results, good agreement has been obtained for the pressure curve, the polar membrane strains and the strain distributions and it has thus been shown that the approach is applicable to the analysis of three-dimensional sheet-metal forming.