横向力作用下的悬臂桁架结构拓扑优化

研究了应力约束下最小重量悬臂梁桁架结构的拓扑优化设计。根据Michell理论,首先用解析方法和有限元方法建立满应力类桁架连续体结构。然后选择其中部分杆件形成离散桁架作为近最优结构,并建立桁架的拓扑优化解析表达式。采用解析方法证明最优拓扑结构的腹杆中间结点在节长的四分之一位置。最后采用解析和数值方法对自由端受集中力和侧边受均布力作用的桁架进一步拓扑优化,确定了桁架的节数和每节的长度,最后得到拓扑优化桁架结构。得到的拓扑优化桁架比工程上普遍采用的45°腹杆桁架的体积少20%以上。

TOPOLOGICAL OPTIMIZATION OF CANTILEVER TRUSS UNDER LATERAL FORCE

Topology optimization design of minimum weight cantilever trusses subjected to stress constraints is studied. First, the fully stressed truss-like continuum structures are established by analytical method and finite element method based on Michell's theory. Second, the continuum structures are discretized to trusses as near optimum structures by selecting parts of members. The topology optimization problems are formulated and solved. It is proved that in the topology optimum trusses, the midst nodes of web members locate at one fourth of the panel length. The trusses subjected to two point forces at their tips and subjected to uniform distribution forces at their sides are optimized by analytical and numerical methods. The optimum numbers and lengths of panels are obtained. These optimum trusses are lighter over 20% than the trusses with web members of 45° , which are frequently used in engineering.