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

An approach using the energy method is proposed for the analysis of th ree-dimensional sheet-metal forming. There are some limitations in ana lysis by the energy method, e.g., the analytical expression of the geo metric configuration and the construction of a proper kinematically-ad missible velocity field are very difficult and the estimation of strai n rate at a point on the surface is very complicated. In the method su ggested, the principal components of strain increment are calculated d irectly from the change of geometric profile for an arbitrary triangul ar element. The corresponding solution is found through optimization o f the total energy consumption with respect to some parameters assumed in the kinematically-admissible velocity field and the geometric prof ile. In order to check the validity of the method proposed, the hydros tatic bulging of an elliptic diaphragm has been analyzed. In compariso n of the computed results with existing experimental results, good agr eement has been obtained for the pressure curve, the polar membrane st rains and the strain distributions and it has thus been shown that the approach is applicable to the analysis of three-dimensional sheet-met al forming.