周期性极小曲面多孔结构在模型轻量化中的建模与优化研究

Porous structure is considered to be one of the most effective way to realize the lightweight of models and improve the applicability of the object. Although traditional porous structures (such as cellular structure and scaffold structure) are easy to manufacture and achieve lightweight, they have the problems of anisotropy and uncontrollability. Responding to these challenges, we intend to solve the problems of lightweight using Porous structure is considered to be one of the most effective way to realize the lightweight of models and improve the applicability of the object. Although traditional porous structures (such as cellular structure and scaffold structure) are easy to manufacture and achieve lightweight, they have the problems of anisotropy and uncontrollability. Responding to these challenges, we intend to solve the problems of lightweight using porous structures of periodic minimal surfaces, which exhibit superior characteristic of smoothness, connectivity and controllability. Then, we propose to investigate the modeling and optimization of lightweight using the porous structures. Also, 3D printing technology is utilized to support the manufacture and test of the complex porous structures. Specifically, we explore the porous structures of three periodic minimal surfaces, which will be further used to build the modeling of lightweight. Then, the optimal mass transportation is utilized to optimize the model. Finally, entity models are produced by 3D printing for laboratory testing and feedback control. This project presents the construction and implementation of an integrated framework consisting of modeling, optimization and feedback control. The project will supply a spectrum of choices for porous structures, provide theoretical guidance for the design and optimization of lightweight, and also expand its applications.

多孔结构被认为是实现模型轻量化，改善对象隔音和透气等适用性的最有效方式之一。然而，研究发现传统多孔结构（如蜂窝结构和支架结构）虽易于加工且能达到轻量化目的，但存在结构各向异性和容易受力集中等缺点。针对上述问题，本项目拟利用具有光滑性、连通性及可控性等诸多优点的周期性极小曲面构造更加适用且可控的多孔结构，并实现该多孔结构在模型轻量化设计中的建模和优化，进一步通过3D打印技术完成该复杂多孔结构的模型制造与检测。具体地，拟探索适用于轻量化的三周期性极小曲面多孔结构，研究该多孔结构在模型轻量化中的建模、基于最优传输理论的精确优化求解，以及通过3D打印技术实现实体化检测和反馈优化控制等关键问题，构建具有“建模-优化-反馈控制”的一整套高效的轻量化设计与实现框架。预期结果将丰富适用于轻量化的多孔结构选择，为高适用性、可控性的轻量化设计与优化提供理论指导，同时拓展轻量化的应用范围。

多孔结构被认为是实现模型轻量化，改善对象适用性的最有效方式之一。传统多孔结构（如蜂窝结构和支架结构）虽易于加工且能达到轻量化目的，但存在结构各向异性和容易受力集中等缺点。此外，传统多孔结构在适用性、可信性及效率性等方面仍存不足，研发多样性多孔结构及高效优化求解是关键。本项目针对上述问题，利用周期性极小曲面构造更加适用且可控的多孔结构，并实现了该多孔结构在模型轻量化设计中的建模和优化，构建了具有“建模-优化-反馈控制”的一整套设计与实现框架。在该项目支持下，项目组四年来在多孔结构轻量化方面进行了深入研究，在基于周期性极小曲面的多孔结构设计和优化方面取得了重要进展，完成了多尺度多孔结构的表示、建模和优化一整套设计与实现工作。提出的多孔结构在工程设计、生物医疗应用、复合材料设计等相关领域的应用探索，部分成果为该领域开拓性工作，填补了相关方面空白。总体上，项目组超额完成项目预期制定任务。相关成果在CCF A类期刊TVCG, B类期刊CAD, CAGD, 以及中科院1区期刊Materials & Design等期刊和会议发表20余篇，授权发明专利6项，申请美国国际专利2项，国内专利2项，完成软件著作权2项，完成1项专利成果转化，培养博士/硕士研究生6人。本项目利用周期性极小曲面多孔结构对模型进行轻量化建模进行了深入探索，奠定了较好的研究基础与前期思路可行性探索。其重要意义在于给现有轻量化方法所面临的问题提供了新的思路和方法，是一个必要的补充和完善。同时也为结构优化的进一步拓展应用和推广做了初步探索，为工程领域及高精工业等方面的应用提供了理论指导和技术支持。