二维桁架结构拓扑优化的特征线提取方法及算例分析

Feature-line Extraction Method for Two-dimensional Truss Structure Topology Optimization

针对二维桁架结构拓扑优化结果面向工程制造的问题,提出了一种桁架拓扑优化结果的特征线(桁架杆件轴线)提取方法。基于渐进结构优化方法(ESO)对连续体结构进行拓扑优化,获得桁架结构的拓扑结构。根据桁架拓扑优化结果提取各拓扑区域的中心点坐标,基于桁架杆件的直线特征对拓扑区域进行区域划分,而后建立各拓扑区域的特征线数学模型。结合各特征线数学模型确定桁架杆件的节点,并引入节点合并的半径区域,建立了桁架各杆件连接节点位置的二次优化数学模型。最终,根据最优的节点位置得到了面向制造的桁架拓扑优化结果-特征线。采用3个经典算例,验证了该桁架拓扑优化结果特征线提取方法的有效性,为后续桁架结构的杆件截面优化提供了基础。

A truss structure topology optimization feature-line（ axis of the turss） extraction method is proposed for the problem of the two-dimensional truss structure topology optimization manufacturing. The continuum structure is optimized based on the evolutionary structural optimization method（ ESO）. The center point coordinates of the topological area are extracted according to the truss topology optimization result. The topological area is divided based on the truss linear characteristics and then the topological area feature-line mathematical model is established. The truss nodes are determined and combined with the feature-line mathematical model and then the radius of the nodes merging area is introduced to establish the truss nodes position quadratic optimization mathematical model. Finally,the truss topology optimization result（ feature-line） oriented to manufacturing is extracted based on the optimal truss node position. Three classical examples are used to verify the effectiveness of the feature-line extraction method.