Analysis of Hydrostatic Bulging of a Rectangular Diaphragm by Using the Energy Method

에너지법에 의한 직사각형 격막의 정수압벌징 해석

The present study is concerned with the analysis of three-dimensional sheet metal forming process by the upper-bound method. For the analysis a systematic approach is necessary for the expression of geometric configuration of the deforming workpiece. In the present paper geometric configuration is constructed by three unit surfaces which are defined by sweeping the vertical section curves and boundary curve. The principal components of strain increment during the process is calculated directly from the change of geometric configuration 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 velocity field and geometric profile. In order to verify the effectiveness of the present method, hydrostatic bulging of a rectangular disphragm is analyzed and the computation by the present method for the geometric shape renders the good result. From the comparison of the present results with the existing experimental results and elastic-plastic finite element solutions, good agreements have been obtained for the pressure curves, polar membrane strains and pressure distributions. The present method can thus be further applied to the analysis of other three-dimensional sheet metal forming processes.

본 연구에서는 3차원 형상의 금형에 의한 박판금속 성형 공정을 에너지법으로 해석함에 있어 스윕곡면(SWeep surface)을 통해 기하학적 형상을 효과적으로 표현하는 방법을 제안하고, 이를 직사각형 격막의 정수압벌징의 해석에 으용하여 이에 의한 결 과를 이미 보고된 자료와 비교함으로써 일반적인 박판 성형공정을 해석하는데 본 이론 의 적용 가능성에 대하여 논의하고자 한다.