Optimum design of the shape of the initial blank is an important task before sheet metal forming processes. It reduces production costs, material waste and improves the quality of the product significantly. In the present work, the blank shape optimization problem is considered based on the 3D space target contours and moreover the sheet metal can have an internal boundary. In other words, the shape optimization process can be applied on the internal boundary, external boundary or both. To the best knowledge of the authors, there are no published works in this subject. Using the iterative simulation-based optimization process, a special shape error index and also updating algorithm were proposed to modify the blank geometry in each iteration until capturing the optimum shape. The sheet forming process is highly nonlinear in nature due to plastic behaviors, large deformations and frictional contact surfaces. Therefore, the updating formula should be robust enough to have less sensitivity with respect to the initial guess. To evaluate the proposed updating formula and its robustness, some numerical examples were considered and the effects of different tools geometries, 2D and 3D target contours, internal and external boundaries and different initial guesses were examined.

初始毛坯形状的优化设计是钣金成型工艺之前的一项重要任务。它降低了生产成本、材料浪费并显着提高了产品质量。在目前的工作中，毛坯形状优化问题是基于 3D 空间目标轮廓考虑的，而且钣金可以有一个内部边界。换句话说，形状优化过程可以应用于内部边界、外部边界或两者。据作者所知，该主题没有已发表的作品。使用基于迭代模拟的优化过程，提出了一种特殊的形状误差指标和更新算法，以在每次迭代中修改毛坯几何形状，直到获得最佳形状。由于塑性行为、大变形和摩擦接触面，板材成形过程在本质上是高度非线性的。因此，更新公式应该足够健壮，以降低对初始猜测的敏感性。为了评估所提出的更新公式及其稳健性，考虑了一些数值示例，并检查了不同工具几何形状、2D 和 3D 目标轮廓、内部和外部边界以及不同的初始猜测的影响。