Development of an inverse isogeometric methodology and its application in sheet metal forming process
Development of an inverse isogeometric methodology and its application in sheet metal forming process
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DOI：
10.1016/j.apm.2019.03.042
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发表时间：
2019-09
影响因子：
5
通讯作者：
M. Shamloofard;A. Assempour
中科院分区：
文献类型：
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作者：
M. Shamloofard;A. Assempour
本文提出了一种逆等几何分析来估计毛坯并预测钣金成形过程中的应变分布。在本研究中，相同的 NURBS 基函数用于绘制最终零件并分析成形过程。换句话说，与逆有限元法相比，这种方法仅需要一种建模和分析表示。该模型涉及势能最小化、塑性变形理论以及考虑新的非均匀摩擦模型的无穷小变形关系。该方法的优点之一是控制方程在二维空间中求解，无需考虑预先估计结果。因此，保证了收敛性并显着减少了计算时间，这在设计的初始阶段非常重要。此外，通过在成形设计阶段采用该模型，可以同时观察改变最终零件几何形状和材料性能对零件成形性的影响。此外，可以自动研究等几何单元尺寸对求解精度的影响。通过三个例子证明了该方法的能力，包括圆柱杯、方箱的毛坯估计以及拼焊毛坯成形中的焊缝移动。通过所提出的模型获得的结果和通过正向有限元获得的结果显示出合理的精度，同时降低了计算成本。
This paper proposes an inverse isogeometric analysis to estimate the blank and predict the strain distribution in sheet metal forming processes. In this study, the same NURBS basis functions are used for drawing a final part and analysis of the forming process. In other words, this approach requires only one modeling and analysis representation, in contrast to inverse FEM. This model deals with minimization of potential energy, deformation theory of plasticity, and infinitesimal deformation relations with considering a new non-uniform friction model. One advantage of the presented methodology is that the governing equations are solved in two-dimensional space without concerning about pre-estimation results. As a result, the convergence is guaranteed and the computation time decreases significantly which is important at the initial stages of design. Furthermore, by employing this model at the forming design stage, the effects of changing the final part geometry and material property can be simultaneously observed on the formability of the part. Moreover, the effects of isogeometric element size can be automatically studied on the solution accuracy. The capability of this method is demonstrated by presenting three examples including blank estimation of cylindrical cup, square box, and weld line movement in forming of tailor welded blanks. The results obtained by the presented model and those obtained by the forward FEM reveal reasonable accuracy with decreased computational costs.