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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。
In this paper, a more in-depth study on smoothing and morphological optimization of grids appearing in the free-form surface space grid structure modeling is carried out. Combining with the meshing technique of the mapping method of bi-cubic quasi-uniform B-spline surface, the smoothness criterion of surface energy method is introduced, and smoothing control of free-form mesh structure is achieved by adjusting the smoothing factor, and the smoothing factor and grid structure Morphological characteristics of the law. On this basis, the multi-objective function of grid shape optimization with smoothing factor as optimal design variable, grid shape quality coefficient, length deviation of bar element and Gaussian curvature as design indexes is proposed. The optimal shape space grid structure obtained by optimization is solved and the principle explanation of the optimization process is given by the solution space. The optimization analysis of several free-form surface space grids in this paper verifies the practicability and reliability of this method.