中文摘要：

自由曲面空间结构不仅要满足特定的几何形态要求,而且需要具备受力均衡的力学性能.结合几何特性分析与力学性能优化,提出了基于自然界中张力薄膜平衡特性的自由曲面空间结构造型技术.将初始的准均匀B样条曲面比拟为张力薄膜,运用拉普拉斯公式与改进的动力松弛法进行优化,得到满足给定边界条件的合理目标曲面.数值实验结果表明,该造型技术简便可行,可有效地缩短自由曲面空间结构的设计周期.

英文摘要：

Free-form space structures should satisfy the specific geometric configuration requirements and have the rational mechanical properties. Combining geometrical characteristics analysis and mechanical properties optimization, this paper proposes a modeling technique for free-form space structures based on equilibrium characteristics of natural tension membrane. To establish the proper objective surface which meets the given boundary conditions, the initial quasi-uniform B-spline surface is treated as tension membrane and optimized by Laplace equation and modified dynamic relaxation method. Numerical experimental results demonstrate that the proposed modeling technique is convenient and feasible, and it is effective for shortening the design period of free-form space structures.