桁架的最小重量设计

Minimum Weight Design of Trusses

结构优化设计的传统方法采用能反映横截面性质的有关量或其倒数作为设计变量,导致了隐函数形式的特性约束,给许多优化解法带来了诸如需要大量的结构重分析和收敛失稳等问题.本文就单工况作用的桁架结构,根据力法分析的思想,提出以多余杆内力和静定基杆应力作为设计变量,形成了具有显式约束的数学规划问题;同时也提出了一种线性化解法,可保证迭代寻优过程收敛的稳定性.整个求解过程不需要结构重分析,不需要灵敏度计算,一般情形下迭代收敛快,可较多地节省计算时间.

The traditional method in optimal design of structures is using sectional properties or their reciprocals as design variables. It results in implicit behavior constraints which cause some problems in a number of optimal algorithms, for instance, a large number of reanalyses of the structure are needed and iterative convergence is instable. Based on the force method of structural analysis, this paper presents an optimal procedure which treats redundants and stresses of a statically determinate basis as design variables. It leads to a mathematical programming with explicit constraints. Also the paper proposes a linearization method which ensures the stable convergence of the iterative process. The whole solution procedure needs neither reanalysis of the structure, nor calculation of sensitivity. Therefore, in general the iterative convergence is fast and calculation is saved considerably.