面向多尺度结构优化设计的MV-CUT水平集方法研究

具有轻质高强、多功能化等优良特性的高性能构件是国家重大装备的核心组成部分，多尺度结构优化是实现高性能构件设计的有效途径。增材制造技术的迅猛发展促使多尺度结构优化设计成为前沿研究热点，但仍存在宏微观结构尺度分离、相邻微结构之间连接性差、计算量巨大和计算效率低下等具有挑战性的问题尚未得到很好的解决，成为制约多尺度结构优化设计的关键因素。本项目拟建立新的宏微观结构尺度关联的MV-CUT（Multiple Variable Cutting）水平集方法，通过将传统微结构设计问题转化为若干切割函数曲面控制问题，确保相邻微结构之间至少具有C0连续性，显著减少设计变量；发展全过程并行的多尺度有限元方法，大幅提升结构分析效率和计算规模；系统研究MV-CUT水平集方法在不同优化问题中的有效性和适用性。研究成果有望进一步推动宏微观结构一体化设计理论和方法的发展，为大规模/高分辨率结构分析和优化设计提供解决方案。

High-performance components with excellent characteristics such as light weight, high strength and multi-functionality are the core components of major national equipment. Multi-scale structural optimization is an effective way to achieve high-performance component design. The rapid development of additive manufacturing technology has made multi-scale structure optimization design a frontier research hotspot, but there are still challenging issues such as macro-micro structural scale separation, poor connectivity between adjacent microstructures, huge calculations, and low calculation efficiency, which are not well resolved and become key factors restricting the optimal design of multi-scale structures. This project intends to establish a new scale-associated MV-CUT (Multiple Variable Cutting) level set method, in which at least C0 continuity between adjacent microstructures will be ensured by translating the traditional optimization design of microstructures into the surface control problem of several cutting functions. This will reduce the number of design variables significantly. In addition, a fully parallel multiscale finite element method will also be developed for improving the computing efficiency and capability. Moreover, we will also systematically study the effectiveness and applicability of the MV-CUT level set method in different optimization problems. Research results are expected to further promote the development of the theory and numerical approaches about integrated design of materials and structures, and provide solutions for large-scale / high-resolution structural analysis and optimization design.