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。
张向奎
,
王峰
,
刘伟杰
,
董亚亚
,
王甜驹
. 多步逆成形有限元法中间构型初始解预示算法[J]. 机械工程学报, 2015
, 51(24)
: 118
-125
.
DOI: 10.3901/JME.2015.24.118
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.
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