长悬臂桁架受横向集中力的拓扑优化

Topological Optimum of Long Cantilever Truss under Transverse Concentrated Load

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.

Topology optimization design of long cantilever truss with minimum weight is derived analytically. A transverse concentrated load is applied at its free end. The truss with constant width is subjected to stress constraints. The panel lengths, nodal coordinates, the angles of the chords, the web members and the cross-sectional areas are taken as design variables. It is proved that there is no difference of the positions and the cross-sectional areas of web members between different panels in topological optimum truss. The middle nodes of web members locate at position of 1/4 of panel length. The topological optimum truss is similar to the truss with web members of 45° when the topological optimum truss tends to infinite long. The difference of volume between truss-like continuum and corresponding discrete truss is slight.