Abstract Laser peen forming (LPF) is a flexible forming process that brings many challenges for complex shaping. This study aims to develop an effective optimization method to complete efficient process planning of LPF to generate the desired geometry shape. The eigen-moment is proposed as a new intermediate variable to describe the bending deformation to relate the LPF process parameters and the geometry shape. The governing equation of eigen-moment is derived to characterize the bending deflection with a PDE equation. The numerical computation method is developed by the PDE weak form and finite element method to predict the bending shape. To achieve process planning of complex shaping, the distributed eigen-moment on both plate surfaces is prescribed, and a PDE-constrained optimization is utilized to define the process planning problem of LPF. Then, the eigen-moment field is optimized by adopting the interior-point algorithm to obtain the desired shape. The proposed eigen-moment is verified to be an intrinsic physical quantity to describe the bending behavior of LPF. A complex shape with saddle geometry is used as a typical case to demonstrate the process planning method. The experiments conducted with the planned LPF process parameters are validated to produce a shape consistent with the designed geometry.

中文翻译：

---

具有分布式特征矩的复杂成形激光喷丸成形的高效工艺规划

摘要 激光喷丸成型（LPF）是一种灵活的成型工艺，给复杂成型带来​​了诸多挑战。本研究旨在开发一种有效的优化方法来完成 LPF 的高效工艺规划，以生成所需的几何形状。本征矩被提议作为一个新的中间变量来描述弯曲变形，从而将 LPF 工艺参数和几何形状联系起来。推导出特征矩的控制方程，用偏微分方程来表征弯曲挠度。数值计算方法是由偏微分方程弱形式和有限元方法开发的，用于预测弯曲形状。为了实现复杂成形的工艺规划，规定了两个板表面的分布特征矩，并利用偏微分方程约束优化来定义LPF的工艺规划问题。然后，采用内点算法对特征矩场进行优化，得到所需的形状。所提出的本征矩被验证为描述 LPF 弯曲行为的内在物理量。以具有鞍形几何形状的复杂形状作为典型案例来演示工艺规划方法。使用计划的 LPF 工艺参数进行的实验得到验证，以产生与设计几何形状一致的形状。