中文摘要：

针对狭长结构拓扑优化过程中存在的计算困难、有中间密度存在和优化构型复杂等问题,提出周期模块拼装方法,并建立混合梁单元模块有限元模型,开展了狭长结构的拓扑优化设计。以承受均布压力载荷的悬臂狭长结构为例,分析比较了不同模块数、不同材料用量以及不同截面梁对优化结果的影响。计算结果显示,采用周期模块拼装策略能获得规则简单易制造的优化构型,周期狭长结构具有尺寸效应且存在最佳模块尺寸来最大化拼装结构刚度。将混合梁单元模型的模块尺寸与拓扑协同优化结合,获得了清晰规则的类桁架构型。最后应用所提方法实现了周期狭长梯形结构的构型优化。

英文摘要：

A repetitive module assembling method and a mixed finite element model were presented where the computational difficulties,intermediate density and complex geometries existed.The influences of repetitive module number,material volume fraction and beam section sizes on optimization results were comparatively investigated on the basis of optimization design of thin-and-long cantilever structure subjecting to uniform pressures.The results show that optimization configuration with regularity,simplicity and easy to manufacture can be obtained by repetitive module assembling method.Size effects of periodic thin-and-long structure are obvious,and there is an optimal module size for periodic thin-and-long structure to maximize stiffness.Regular truss-like configuration of repetitive module is obtained with concurrent optimization of both module size and layout,based on mixed finite element model.Finally,topology optimization of a thin-and-long trapezoidal cantilever structure was achieved using the proposed method.