桁架结构拓扑及截面尺寸优化设计方法

周奇才; 吴青龙; 熊肖磊; 王璐

doi:10.7652/xjtuxb201609001

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桁架结构拓扑及截面尺寸优化设计方法

更新时间：2025-07-09

- 桁架结构拓扑及截面尺寸优化设计方法
- Optimal Design of Topology and Section Size of Truss Structures
- 西安交通大学学报 2016年50卷第9期页码：1-9
- 作者机构：
  
  同济大学机械与能源工程学院,上海,201804
- 作者简介：
- 基金信息：
  
  : 2016-02-25。作者简介: 周奇才(1962—),男,教授,博士生导师。基金项目: 国家自然科学基金资助项目(51375345)
- DOI：10.7652/xjtuxb201609001
  中图分类号： TH11
- 网络首发：2016-09-10，
  
  纸质出版：2016
- 稿件说明：
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周奇才, 吴青龙, 熊肖磊, 等. 桁架结构拓扑及截面尺寸优化设计方法[J]. 西安交通大学学报, 2016,50(9):1-9.

Optimal Design of Topology and Section Size of Truss Structures[J]. 2016, 50(9): 1-9.
周奇才, 吴青龙, 熊肖磊, 等. 桁架结构拓扑及截面尺寸优化设计方法[J]. 西安交通大学学报, 2016,50(9):1-9. DOI： 10.7652/xjtuxb201609001.

Optimal Design of Topology and Section Size of Truss Structures[J]. 2016, 50(9): 1-9. DOI： 10.7652/xjtuxb201609001.

摘要

为克服传统基结构设计方法对最优解的束缚

实现桁架结构的拓扑布局及尺寸优化

提出了将连续体与离散杆系相结合的桁架结构优化设计方法。从连续体出发

基于SKO连续体拓扑优化方法得到了最优拓扑布局; 以二值图像细化算法为基础

提出了基于有限单元8邻域网格模型的骨架提取算法

通过剥离冗余单元

得到了连续体拓扑优化结果的中心传力骨架; 以单元主应力为判据

精确找到骨架中的关键点

并连接关键点形成了初始桁架结构; 基于拉格朗日乘数法和Kuhn-Tucker条件

以初始桁架中杆件的内外半径为设计变量

结构体积为约束条件

结构柔度为目标函数

建立了桁架结构杆件尺寸优化的数学模型

并推导出其优化迭代准则。最后

以一悬臂结构为例对该优化方法的应用进行了说明

并使用一经典算例与其他文献中的方法进行了对比

结果表明:该优化方法得到的桁架结构具有优化的拓扑构型和力学特性

杆件布局、尺寸合理

应力均匀。

Abstract

To achieve the topology and section size optimization of the truss structures without being restricted by the traditional ground structure method

a new optimization method combining continuum with discrete bars is proposed. Starting from continuum and using SKO topology optimization method

an optimal topological layout is obtained. Then based on the FEM 8-neighbourhood elements and binary image thinning method

a skeleton extraction algorithm is put forward to remove the redundant element of the optimal topology and get its central force flow skeleton. Through principal stress calculation of the elements

the key points of the skeleton are found precisely

and the initial truss structure is obtained by connecting these key points. For the optimization of bar section size

a mathematical model is established using section sizes as the design variables

truss volume as the constraint condition and truss flexibility as the objective function. And based on this model the optimization criteria are derived according to the Lagrange multiplier method and Kuhn-Tucker condition. Finally this truss design method is illustrated and verified by two examples. Results show that the optimal structures achieve excellent layout

appropriate bar section sizes and uniform stress distribution.

关键词

Keywords

references

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