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用解析方法推导拓扑优化最小重量长悬臂桁架.桁架在应力约束下,自由端受横向集中力作用,桁架宽度为常数,它的节长、结点坐标、腹杆和弦杆的角度,以及所有杆的横截面尺寸均为设计变量.分析结果表明,拓扑优化桁架中的各节腹杆的位置和横截面面积相同,中间结点位于每节1/4位置.当结构长度趋于无限长时,腹杆趋于30°,60°,相对45°桁架的体积差别不大,与类桁架连续体的体积差别也很小.
The analytic method is used to deduce the topology optimization of the minimum weight long cantilever truss. Under the constraint of stress, the free end is subjected to horizontal concentrated force, the truss width is constant, its node length, node coordinates, web and chord angle, The results of the analysis show that the location and cross-sectional area of the webs in the topological optimization truss are the same, and the intermediate nodes are located in each quarter of the section.When the length of the structure tends to infinity, Belly tendons to 30 °, 60 °, relative to the 45 ° truss volume difference is not large, and the type of truss continuum volume difference is also small.