中文摘要：

运用一种基于全量理论的多步有限元方法计算分析了金属体积成形过程．该方法针对刚塑性不可压缩材料，在静力平衡条件下以约束变分原理通过最小化近似塑性势能进行有限元求解．多步模拟在各中间构形的虚拟滑动约束下沿变形路径进行分步迭代计算，考虑了接触和变形历史，能够快速模拟较复杂的体积成形问题．运用该方法对几个典型金属体积成形过程进行了正向一步和多步数值模拟，将计算结果与增量有限元法计算结果进行了比较．结果表明：在计算金属体积成形过程中，基于全量理论的多步有限元模拟能够在大火缩短计钟．时间的同时获得与增量法计算结果相比偏差小于10％的计算结果．

英文摘要：

The bulk metal forming processes are calculated and analyzed by using a multi-step finite element method （FEM） based on deformation theory of plasticity. In this method, FEM solution is implemented to minimize approximated plastic potential in static equilibrium by constraint variation principle, for incompressible rigid-plastic materials. The multi-step simulation deals with the fictitious sliding constraints for intermediate configurations and iterations step by step along the deformation path, considering the contact and deformation history, which could provide rapid analysis for more complicated bulk forming problems. The one step and multi-step forward simulations of several typical bulk metal forming problems are performed by this method, the calculated results of which are compared with those obtained by incremental FEM. The results indicate： multi-step FEM simulation of the bulk metal forming processes could give the reasonable answers with a small amount of computing time, the errors of which are less 10% compared with those of incremental FEM.