增材制造填充与支撑结构拓扑和参数自适应优化的计算几何学理论及技术研究

Lightweight Design for complicate 3D models is of significant importance for saving material and improving productivity in Additive Manufacturing. Given manufacturing material and build direction, guaranteeing surface quality and model strength, maximizing the strength-to-weight ratio of the infill structure and minimizing the weight of the support structure are very critical for lightweight design. Under a fixed external pressing/pulling force, with the infill space of the model being partitioned by a set of cubes, this project optimizes the strength-to-weight ratio of a hybrid of the infill patterns and their geometric parameters based on the Monte Carlo Method and the edition of the cubes. Guaranteeing the supported surface quality, based on the discretization of the intersections of a set of cones rooted at the tree nodes and the Monte Carlo Method, this project also focuses on the minimization of the line segment length of the topology, and the geometric parameters of the tree-shaped support structures. This research lays the theory foundation for the additive manufacturing of products with guaranteed strength and surface quality while minimizing the material used, and is of significant impact on the research direction of lightweight modeling in the field of Additive Manufacturing.

增材制造复杂三维模型的轻量化设计对节省制造材料，提高制造效率具有重要意义。给定制造材料和制造方向，在保证模型外表面形状不变和强度满足要求的条件下，模型内部填充结构强度-重量比最大化以及制造过程所需支撑结构的重量最小化是实现增材制造模型轻量化的关键。在外部一定的压力/拉力作用下，利用模型空间的立方体单元格化剖分，以强度-重量比最大化为目标，基于蒙特卡罗方法和立方体单元格编辑方法研究多种填充模式的组合优化和几何参数最优化。在保障模型表面质量条件下，基于以树的节点为顶点的圆锥体相交区域离散化采样和蒙特卡罗方法，本项目研究树状支撑结构树枝节点连接拓扑结构总长度以及树枝尺寸的最小化问题。该研究为增材制造中使用最少材料生产出强度和表面质量符合要求的产品提供理论和技术基础，对轻量化几何建模这一增材制造学术研究领域发展具有重要意义。

本课题围绕增材制造几何模型填充与支撑结构拓扑和参数自适应优化，展开相关计算几何学理论及技术研究。依托基金支持，发表或已接收的第一作者或通讯作者SCI国际期刊论文7篇，主要刊发于IEEE TVCG, ASME JMD等计算机图形学、机械设计领域顶级期刊；成功申请实用新型专利1项。培养2名博士生3名硕士生，其中1名博士生已毕业。该研究为增材制造中使用最少材料生产出强度和表面质量符合要求的产品提供理论和技术基础，对轻量化几何建模这一研究领域发展具有重要意义。

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