中文摘要：

该文对自由曲面空间网格结构造型中出现的网格光顺与形态优化问题进行了较为深入的研究。结合双三次准均匀B样条曲面的映射法网格划分技术，引入曲面能量法光顺准则，通过光顺因子的调整进行自由曲面网格结构的光顺控制，并得到光顺因子与网格结构形态特性的影响规律。在此基础上，提出以光顺因子为优化设计变量，以网格形状质量系数、杆件单元长度偏差及高斯曲率特征为设计指标的网格形态优化的多目标函数。经优化求解得到所需的最优形态空间网格结构，并由解空间给出优化过程的原理性解释。该文中若干自由曲面空间网格结构的优化分析验证了该文方法的实用性与可靠性。

英文摘要：

The thorough study on the fairing and configuration optimization of free-form space grid structures is presented. Combined with mapping technology of bicubic quasi-uniform B-spline surfaces, the energy method is introduced to smooth free-form space grid structures through a fairing factor adjustment, and the effects of a fairing factor on morphological characteristics of a grid structure are investigated. On this basis, the fairing factor is set as the design variable, and the multi-objective optimum function, whose objective variables are the quality factor of a grid form, the tolerance of elements length, and the characteristic of Gaussian curvature, is proposed. The optimum configuration of a space grid structure is finally achieved from the solution of a multi-objective optimum function, and the nature of the optimum process is interpreted by the solution space. The analyses of several free-form surface grid structures verify the practicality and reliability of the method discussed in the paper.