多工况下空间框架结构最小柔顺度拓扑优化

Minimum Compliance Topology Optimization of Space Frame Structures Under Multiple-loading Cases

针对多工况作用下以柔顺度最小化为目标和体积为约束的空间框架结构拓扑优化问题,设计了一种新的优化思路。首先,利用Hypermesh软件和基结构法构建空间框架结构基础模型。其次,选用空心圆柱形梁单元,并以梁单元横截面外直径的平方为设计变量;采用加权和方法处理多工况作用下的结构柔顺度,构建以体积为约束的拓扑优化初始模型,运用变体积约束限措施将初始模型进行等效近似转换。然后,对结构柔顺度和体积进行灵敏度分析,并采用移动渐近线法(MMA)进行优化求解。最后,通过两个优化算例验证了所提方法是正确可行且有效的,为空间框架结构的优化设计提供参考。

Aiming at the topology optimization problem of space frame structures with minimum compliance as the target and volume as the constraint under multiple load cases,a new optimization idea is proposed.Firstly,Hypermesh software and ground structure method are used to build the basic model of space frame structures.Secondly,the hollow cylindrical beam element is selected,and the square of the outside diameter of the beam element is taken as the design variable.The weight sum method is used to deal with the structural compliance under multiple-loading Cases,and the initial topology optimization model with volume constraint is constructed.The equivalent approximate transformation of the initial model is carried out using a varying volume limit scheme.Then,the sensitivity of the structure compliance function and volume function are calculated,and the proposed topology optimization problem is solved by the method of moving asymptotes(MMA).Finally,the proposed method is verified to be correct,feasible and effective by two optimization examples,which provides a reference for the optimization design of space frame structures.