空间网格结构基于离散变量的优化设计

空间网格结构离散变量的优化设计是空间网格结构的截面尺寸优化、形状优化、拓扑优化和布局优化的理论基础。本文在建立空间网格结构离散变量优化设计问题数学模型的基础上，分析了空间网格结构离散变量优化设计的特点和算法效率。文中采用相对差商法。对空间网格结构杆件截面尺寸的离散变量优化设计问题进行了研究和探讨。文章最后给出了两个算例，计算结果验证了本文理论的正确性和有效性。

OPTIMAL DESIGN OF LATTICE STURCTURES ON DISCRETE VARIABLES

The optimal design of lattice structures includes the size optimization, the shape optimization, the topology optimization and the layout optimization, which all based on the optimal theories with discrete variables. In this paper, some elementary studies on optimal design of lattice structures on discrete variables are discussed. After establishing the mathematical model of lattice structures, some important characteristics on those optimal problems are analyzed. A new optimal method with discrete variables _ Relative Difference Quotients Method is suggested to solve the problem of the size optimization. At the end, through a lot of numerical examples, the theories above are tested and verified to be correct. [