抗屈曲的柔性机构拓扑优化设计

Topology Optimization Design of Anti-Buckling Flexible Mechanism

针对柔性机构拓扑优化中的稳定性问题与特有的铰链问题,本文提出了一种考虑线性屈曲约束且不含铰链的拓扑优化求解方法。首先,基于Pian单元,引入柔顺度变化率约束,以解决柔性机构的铰链问题;其次,结合KS(Kreisselmeier-Steinhauser)凝聚函数与线性屈曲方程给出线性屈曲约束的推导;最后,结合线性屈曲约束、柔顺度变化率约束,建立一种考虑线性屈曲约束且不含铰链的拓扑优化模型,并结合移动渐近线方法(Method of Moving Asymptotes,MMA)有效求解。给出的算例结果表明,该方法能够对结构临界屈曲载荷进行有效约束。

Aiming at the stability problem and the unique hinge problem in the topology optimization of flexible mechanisms,this paper proposes a topology optimization solution method that considers linear buckling constraints and does not contain hinges.First,based on the PIAN unit,the compliance change rate constraint is introduced to solve the hinge problem of the flexible mechanism;then,combining the KS aggregate function and the linear buckling equation,the derivation of the linear buckling constraint is given;dinally,combining linear buckling constraints and compliance change rate constraints,a topology optimization model considering linear buckling constraints without hinges is established,and combined with MMA(Method of Moving Asymptotes)algorithm for effective solution.The results of the given examples show that the method can effectively restrain the critical buckling load of the structure.