基于等几何分析的结构拓扑优化设计方法研究

Merging the isogeometric analysis (IGA) and structural optimization is an important new direction for the field of computational mechanics, which needs the deepened research. This project aims to establish and develop the optimization model, design method and efficient algorithm of the IGA-based topology optimization design of structures considering the static and dynamic reliability. Firstly, the key formulation and efficient approach of the IGA-based integrated topology and shape optimization of structures are proposed to unify the design process, due to the fact that the existing topology optimization approaches are mainly based on the implicit solution framework, and the emerging explicit approaches have not closely combined CAD and CAE yet. Subsequently, to enhance the computational accuracy and design efficiency, the isogeometric optimization method of simultaneous material and topology design for functionally graded shell structures is developed with achieving the integration of topology and shape optimization, and simultaneous design of material and structure. Finally, the hybridizable discontinuous Galerkin IGA method is proposed through developing the theory of probability density evolution, and the method of stochastic mechanics analysis and algorithm of reliability-based topology optimization of structures with high efficiency and good stability are devised. Moreover, the innovative optimal topology designs of uncertain continuum structures of plates and shells are obtained, and the propagation mechanism of random uncertainty is revealed. This project studies deeply the topology optimization methods of structures combining with the thriving theory of isogeometric analysis, which has important scientific significance and application value for development of industrial digitalization design technology and the relevant program and software.

等几何分析与结构优化的融合是计算力学领域重要的新方向，亟待深入研究。本项目旨在构建与发展基于等几何分析、考虑静动力可靠度的结构拓扑优化设计的优化模型、设计方法和高效算法。首先，鉴于已有的拓扑优化方法主要基于隐式设计框架，新兴的显式方法尚未紧密结合CAD和CAE，提出基于等几何分析的结构拓扑与形状集成优化设计的关键列式和高效方法，形成统一的设计过程。其次，为提高计算精度和设计效率，发展功能梯度壳体结构的材料和拓扑同步等几何优化方法，实现拓扑和形状的集成优化、材料和结构的一体化设计。最后，发展概率密度演化理论，提出混合间断伽辽金等几何方法，建立高效、稳定的结构随机力学分析方法和可靠度拓扑优化算法，获得不确定性板壳连续体拓扑优化创新方案，并揭示随机不确定性传播机理。本项目结合蓬勃发展的等几何分析理论，深入研究结构拓扑优化设计方法，对工业数字化设计技术和程序软件研发具有重要的科学意义和应用价值。