基于自适应成长法的周期性加筋结构拓扑优化设计方法

Topology Optimum Design Method for Periodic Stiffener Structures Based on Adaptive Growth Method

将自适应成长法应用到周期性加筋结构的拓扑优化设计中,以结构的应变能最小为目标,以加强筋截面积为设计变量,并构建拓扑优化设计模型。为保证优化结构可得到周期性最优拓扑形式,在优化数学模型中加入了周期性约束,并引入敏度过滤函数解决数值不稳定等问题。典型工程结构设计案例表明,提出的方法在周期性加筋结构设计中可得到形态清晰的筋条布局,且设计效率高、适用性广。同时利用所提方法模拟荷叶叶脉生长,获得了与自然界荷叶叶脉相似的布局形态,表明自然界荷叶叶脉分布能使荷叶在承受雨雪等自然载荷作用下的整体刚度最大。

Adaptive growth method was applied to topology optimum design for periodic stiffener structures,the minimum strain energy of the structures was taken as the target and the stiffener sectional areas were taken as the design variables,and the topology optimum design model was constructed.In order to ensure the optimize structures might obtain periodic optimal topological form,the periodic constraints were added to the optimization mathematical model and the sensitivity filter function was introduced to solve the problems of numerical instability.The typical engineering structure design examples show that the proposed method may be used to obtain clearly shaped layouts of the stiffener bars in the periodic stiffener structure design,moreover the design efficiency is high and the applicability is wide.Meanwhile,the proposed method was used to simulate the growth of lotus leaf veins,and the layout forms similar to that of natural lotus leaf veins were obtained,which show that the distributions of leaf veins in nature may make the lotus leaf have the maximum overall stiffness under natural loads such as rains and snows.