多步逆成形有限元法中间构型初始解预示算法

Solving Algorithm of Initial Guess of Intermediate Configuration in Multi-step Inverse Finite Element Method

在逆成形有限元法中,为考虑加载路径的影响,针对不同成形类型阶段引入中间构型,整个过程被划分为多阶段成形过程,即多步逆成形有限元法,一个好的中间构型初始解的构造是其中的关键问题之一。针对中间构型初始解的构造,提出一种基于滑移约束曲面的节点反向映射法:利用板材的纯几何弯曲效应构造出弯曲构型,经过伪最小面积法优化后生成空间滑移约束曲面;投影展平的最终构型网格面到展平滑移约束曲面网格中,利用面积坐标计算出所有投影节点的坐标;投影节点反向映射回到空间滑移约束曲面上,构造出对应中间构型的初始解。另外,针对中间构型初始解构造中可能出现部分节点无投影区域的问题,给出一种扩展空间滑移约束曲面轮廓的解决方法。零件的数值算例验证相应算法的可行性与有效性。

In order to take loading path into account,intermediate configurations are introduced into different forming stages in inverse finite element method（IFEM）,multi-step IFEM is presented.Research on multi-step IFEM,a good initial guess is one of key links in the process of solving.So,a kind of reverse mapping method,which is based on sliding constraint surface,has been put forward：Firstly,bending configuration is solved through bending effect of blank and sliding constraint surface is obtained in pseudo minima area optimization algorithm;Then,all nodes in the unfolded final configuration are projected onto the unfolded sliding constraint surface;Thirdly,all projected nodes will be reversely mapped back to sliding constraint surface after these coordinates are calculated in area coordinate.As a result,the corresponding initial guess of intermediate configuration can be obtained.In addition,for the problem of some nodes without projective region in unfolded sliding constraint surface,a solving solution of extending sliding constraint surface is presented.Numerical simulations validate the effectiveness of the algorithm.