桁架结构尺寸和形状、拓扑的渐进优化方法

提出了一种求解桁架结构尺寸，形状和拓扑组合优化的渐进优化方法。将优化问题分解为拓扑优化和尺寸、形状优化两个子问题分层求解。通过连续化的拓扑变量和近似方法构造了拓扑变量灵敏度系数计算式，由拓扑变量灵敏度系数识别和删除杆件单元。结构尺寸、形状优化采用准则法和渐进移点法的组合方法。分层优化时，在桁架中加上所有可能的杆件，先进行尺寸、形状优化，再进行拓扑优化，随后二者交替进行迭代，迭代过程的结构重量最小值即为最优解。算例表明了文中方法的有效性，以及组合优化最优解不一定是杆件数目较少的解。

Combined Sizing,Shaping and Topology Optimization of Truss Structure Using Evolutionary Structure Optimization

Ref.8 did sizing and shaping optimization of truss structure using evolutionary structure optimization. We believe that in addition to sizing and shaping, topology should also be included in optimization process as such addition can get much better optimization results. In this paper, we present an evolutionary optimization method to combine sizing, shaping and topology design of truss structure with aim of weight minimum. The structure is subject to stress, local buckling and displacement constraints. We optimize three types of design variables:(1) as regards sizing/shaping-variables optimization, we do what Ref.8 did; a full stressed design (FSD) and scaling techniques are applied to sizing variables; the evolutionary node shift method is applied to shaping variables; the two variables are optimized together; (2) the evolutionary killing method, proposed, explained and named by us, is applied to topology variables. An alternating procedure is utilized to couple the three types of design variables and combine the results. The optimum solution is the smallest weight structure in the whole evolutionary process. A 12-element truss, as numerical example, confirms the validity of the method. This example also shows that the optimum solution is not usually the structure with the least elements.