有限元逆算法及其在板料成形工艺优化中的应用

采用三角形单元开发了精度较高的有限元逆算法，算法中考虑了摩擦、压边力、拉深筋、背压力、曲压料面等实际工艺条件．方程组求解引入快速求解算法，比一般的LDLT解法快几倍，尤其对于大型复杂冲压件问题来说求解效率提高更多．用此算法对典型的L型件进行了模拟，并与增量算法和实验结果进行了比较．可以看出该算法已经达到很高的精度，而且模拟过程迭代收敛速度快，计算时间很短．在此基础上以工件的厚向应变作为目标函数，采用一种实用性很强的工艺参数快速优化算法，即黄金分割法对压边力进行优化．仍以L型件为例，优化过程的计算时间说明快速优化算法相对传统增量算法具有明显的优势．

The FE inverse approach and the optimization of process parameters in sheet metal forming

The modified inverse method of finite element is introduced in this paper, which is based on triangle element model. The process parameters such as friction, holding force, curve binder and drawbead are precisely considered in the method. A new fast-solving arithmetic is also introduced into the method,which is much faster than traditional LDLT one and more effective for the application of large stamping piece forming simulation. Based on the modified inverse method, a new practical optimization method is developed for the optimization of holding force, in which the thinning strain is used as the objective function.The optimization case shows that the solving time of the optimization method is much shorter than that of other methods with the same optimization precision.