基于等几何裁剪分析的拓扑与形状集成优化

提出了将设计和分析、拓扑与形状优化集成的思想，探索了基于等几何裁剪分析的拓扑与形状集成优化设计算法，该方法统一了结构优化的计算机辅助设计、计算机辅助工程分析和优化设计的模型，基于B样条的等几何裁剪分析既能准确表达几何形状，又可以用裁剪面分析方便处理任意复杂拓扑优化问题，由裁剪选择标准确定合理的拓扑结构变动方向，结构变动时无需重新划分网格，设计结果突破初始设计空间的限制，还可方便优化形状。建立了等几何裁剪灵敏度分析的计算方法，给出了等几何裁剪分析拓扑与形状集成优化算法，通过典型实例表明所用方法的正确性和有效性。

Integration of Topology and Shape Optimization Design of Continuum Structure Based on Isogeometric Trimmed Surface Analysis

This paper presented an integration idea of computer aided design computer aided engineering analysis, topology and shape optimization design and then explored a kind of optimization strategy for integation of topology and shape optimization design of continuum structure based on isogeometric trimmed surface analysis.The proposed method unified the model of computer aided design, computer aided engineering and optimization design in structure optimization. Isogeometric trimmed surface analysis based on B splines not only expressed the geometry shape accurately, but also solved arbitrarily complex topology optimization problem. The trimmed criteria selected determined the reasonable direction of topology changes. It did not need to remesh during structural optimization process. The design results broke through the limitations of initial design space. It was also convenient in shape optimization. The integration method contained the calculation method for sensitivity analysis of isogeometric trimmed surface, and the algorithm for integation of topology and the shape optimization design based on isogeometric trimmed analysis. A numerical example illustrated the correctness and effectiveness of the method.