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本文采用有限元方法建立了一种非稳态材料塑性成形过程的灵敏度分析理论和模具形状优化设计方法。采用三次Ｂ样条函数描述预成形模具形状，Ｂ样条函数的控制点坐标（系数）作为优化设计变量，通过对控制点坐标的优化设计，使实际终成形件形状与理想终成形件形状之间的差别最小，从而实现预成形模具形状的优化设计，详细建立了目标函数、有限元节点坐标、节点速度对优化设计变量的解析灵敏度方程及其彼此之间的数学关系，并给出了节点速度灵敏度的边界条件
In this paper, a finite element method is used to establish a sensitivity analysis theory and a shape optimization design method for plastic forming of unsteady materials. The cubic B-spline function is used to describe the shape of the preforming mold and the control point coordinates (coefficients) of the B-spline function as the optimal design variables. Through the optimal design of the coordinates of the control points, the shape of the actual final forming piece and the ideal final forming piece The difference between the shapes is the smallest, so as to optimize the shape of the preforming mold. The analytic sensitivity equations of the objective function, the coordinates of the node and the node speed on the optimal design variables are established in detail and their mathematical relationships are given. The node speed sensitivity of the boundary conditions