板料成形多步反向模拟法的中间构型与运动约束

考虑到一步反向模拟法无法考虑变形历史的影响、无法计算各中间步之间的应变等信息,文章提出一种新型的多步反向模拟法。根据当前工步凸凹模信息,采用最小面积法,并结合可行域二次序列规划算法(FSQP)快速获取当前工步零件的构型。提出一种基于重心坐标的穿越搜索策略来提高接触搜索速度,计算复杂度仅为O(n1/d)(d为网格所在空间的维数)。提出的快速接触搜索算法来实现中间构型各个节点在约束滑移面上的移动,其理论成果成功地在自行开发的板料成形反向模拟法软件InverStamp/Multi-step模块中实现。在圆筒形件多步拉深实例中,通过中间工序及最终成形零件厚度分布与基于增量理论的LS-DYNA求解器计算结果的比较,验证了多步反向模拟法的有效性。

Kinematic relations and constitutive equations of multi-step inverse finite element method in sheet metal forming

Because of the shortcomings of the traditional one-step inverse finite element method:no consideration of the effect of deformation history,incapacity to get the strain distribution of intermediate configurations,a novel multi-step inverse finite element method based on the principle of virtue work is proposed.Based on the known configurations of punch and die of the current step,the strategy of area minimization coupled with Feasible Sequential Quadratic Programming(FSQP) code is used to obtain initial intermediate configurations.An efficient walk-through point location algorithm with its complexity O(n1/d) per point (d means the space dimension) is used to deal with contact searching problem and restrain the movement of corresponding nodes of intermediate configurations.Above mentioned improvements are implemented in our in-house inverse analysis software InverStamp/Multi-step module.The presented algorithms are applied to a 2-step deep drawing product.The obtained thickness distributions of intermediate and final configuration have been compared with that of explicit dynamic incremental FEM solver LS-DYNA to evaluate the effectiveness of the proposed algorithms.