基于等几何分析的结构优化设计研究进展

结构等几何分析是计算固体力学领域一种新兴的数值方法，致力于将CAD（计算机辅助设计）和CAE（计算机辅助工程）纳入到统一的数学表达框架。等几何分析紧密联系几何信息，采用相同的数学表达将几何精确建模、结构分析和设计过程结合，为结构优化设计提供了新的选择和机会。相比基于有限元的结构优化方法，等几何优化设计方法可在一定程度上提高结构优化的精度、效率和便利性。本文针对具有代表性的结构等几何优化设计，包括形状优化、尺寸优化和拓扑优化等问题，系统梳理和综述了主要的等几何优化方法及其在结构优化设计中的应用。比较分析和评述了结构等几何优化设计方法的算法特点及计算优势与劣势，探讨了基于等几何分析的结构优化研究的前沿问题，并展望了未来的发展方向，包括：基于复杂剪裁CAD几何的高效等几何分析与优化设计、基于实体几何构造的结构等几何分析和优化设计、等几何分析与其他力学分析方法结合的结构优化、基于等几何分析的壳体优化设计、基于等几何分析的材料和结构一体化优化设计以及考虑不确定性的结构等几何优化设计等。

Research Advances in Isogeometric Analysis-based Optimum Design ofStructural

Isogeometric analysis of structure is an emerging numerical method in the field of computational solid mechanics, and it aims to integrate the computer-aided design (CAD) and computer-aided engineering (CAE) in a unified mathematical expression framework. Isogeometric analysis (IGA) is closely related to the geometric information, which combines the exact geometric modelling with structural analysis and design process, and provides a new choice and opportunity for structural design optimization. Compared with the finite element analysis-based optimization approach, the isogeometric analysis-based design optimization approach can improve solution accuracy, efficiency and convenience to some extent. For the representative isogeometric design optimization problems involving shape, size and topology optimization, this paper systematically summarizes the main isogeometric analysis-based optimization approaches and their applications in optimum structural design. Moreover, the characteristics of algorithm and the corresponding computational advantages and disadvantages of isogeometric analysis-based optimization approaches are comparatively analyzed and reviewed, and some frontier issues of the IGA-based structural optimization are discussed. Meanwhile, the development directions of future research on the IGA-based structural optimization are presented, such as the efficient IGA and optimum design based on the complex trimming CAD geometry, the IGA and optimum design of structure based on the constructive solid geometry, the optimum structural design by combining IGA with other mechanical analysis methods, the IGA-based optimum design of shell, the IGA-based integrated optimum design of material and structure, and the IGA-based optimum design considering uncertainties, etc.