避免MCVC结构拓扑优化模型出现机构的方法

为了避免带体积约束的柔顺度最小化(minimum compliance with a volume constraint,MCVC)模型出现机构,借助带位移约束的重量最小化(minimum weight with a displacement constraint,MWDC)模型,寻找MCVC模型中安全可靠的物理的或者结构性能的参数阈值.99行程序和120行程序分别被用来求解MCVC和MWDC模型.通过对大量出现机构的病态算例进行研究分析发现,当迭代过程中的最大应变能比小于某个阈值时,或者当体积比大于某个阈值时,就可避免机构出现.然而,这2个阈值是依赖于问题的,即对于不同的结构与/或载荷工况,这2个阈值均会取不同的值.在本文测试的算例中,最大应变能比阈值的范围为4.59~12.38,体积比阈值的范围为0.15~0.26.

Approaches of Avoiding Structural Topology Optimization Yielding Mechanisms by the MCVC Model

To address the issue of yielding mechanisms while using the minimum compliance with a volume constraint( MCVC) model,the minimum weight with a displacement constraint( MWDC) model is used to find safe robust thresholds of physical and performance parameters for the MCVC model avoiding mechanisms. The 99-line and 120-line topology optimization codes are used to solve the MCVC and MWDC models,respectively. A large number of morbid examples with mechanisms appearance are studied. Results show that the mechanism occurs when the maximum strain energy ratio is larger than a threshold,or when the volume ratio is less than a threshold. However,the two thresholds are problem dependent. They vary for different structures and /or loading cases,but for those examples that were tested,the range of the threshold of the maximum strain energy ratio turns out to be between 4. 59 and12. 38,and the range of the threshold of the volume ratio is between 0. 15 and 0. 26.