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采用多点逼近遗传算法的屈曲约束下桁架拓扑优化

崔慧永 黄海 安海潮

崔慧永, 黄海, 安海潮. 采用多点逼近遗传算法的屈曲约束下桁架拓扑优化[J]. 机械科学与技术, 2019, 38(1): 121-128. doi: 10.13433/j.cnki.1003-8728.20180103
引用本文: 崔慧永, 黄海, 安海潮. 采用多点逼近遗传算法的屈曲约束下桁架拓扑优化[J]. 机械科学与技术, 2019, 38(1): 121-128. doi: 10.13433/j.cnki.1003-8728.20180103
Cui Huiyong, Huang Hai, An Haichao. Truss Topology Optimization with Buckling Constraints Solved by Multi-point Approximation and Genetic Algorithm[J]. Mechanical Science and Technology for Aerospace Engineering, 2019, 38(1): 121-128. doi: 10.13433/j.cnki.1003-8728.20180103
Citation: Cui Huiyong, Huang Hai, An Haichao. Truss Topology Optimization with Buckling Constraints Solved by Multi-point Approximation and Genetic Algorithm[J]. Mechanical Science and Technology for Aerospace Engineering, 2019, 38(1): 121-128. doi: 10.13433/j.cnki.1003-8728.20180103

采用多点逼近遗传算法的屈曲约束下桁架拓扑优化

doi: 10.13433/j.cnki.1003-8728.20180103
基金项目: 

国家自然科学基金项目说 11672016

详细信息
    作者简介:

    崔慧永(1992-), 硕士研究生, 研究方向为飞行器结构设计与优化, 飞行器总体设计, cuihuiyong@buaa.edu.cn

    通讯作者:

    黄海, 教授, 博士生导师, hhuang@buaa.edu.cn

  • 中图分类号: O302;O342

Truss Topology Optimization with Buckling Constraints Solved by Multi-point Approximation and Genetic Algorithm

  • 摘要: 基于线弹性屈曲理论,讨论了杆单元建模及欧拉单杆失稳判据在桁架结构稳定性分析中的缺陷。为更精确地获得桁架屈曲响应,建议以梁单元进行有限元建模,并利用特征值屈曲分析来获取结构各阶失稳载荷因子及屈曲模态。分析了从基结构法出发求解特征值屈曲约束下桁架拓扑优化问题所存在的求解困难与奇异性。为有效求解该类问题,采用了多点逼近遗传算法,对离散拓扑变量和连续尺寸变量进行了联合优化。同时,通过屈曲模态识别、删除杆件屈曲模态过滤、局部约束临时删除等措施,特征值约束下的求解困难和删除杆件在优化过程中的不利影响也得到了克服。数值算例验证了本文结构建模及优化方法的有效性,同时也表明了该方法具有较高的效率,能够凭借较少的结构分析次数来获得优化解。
  • 图  1  十杆平面桁架几何示意

    图  2  杆单元建模屈曲分析结果

    图  3  梁单元铰接建模屈曲分析结果

    图  4  梁单元刚接建模屈曲分析结果

    图  5  十杆平面桁架前三阶屈曲因子随杆10截面积变化曲线

    图  6  A处十杆平面桁架前三阶屈曲模态

    图  7  B处十杆平面桁架前三阶屈曲模态

    图  8  C处十杆平面桁架前三阶屈曲模态

    图  9  模态识别与屈曲约束函数序列示意

    图  10  十杆平面桁架重量迭代曲线

    图  11  十杆平面桁架优化后前两阶屈曲模态

    表  1  十杆平面桁架结构参数

    几何参数h 载荷P 截面积 弹性模量 泊松比
    914.4 cm 50 kN 100 cm2 68.96 Gpa 0.3
    下载: 导出CSV

    表  2  删除杆件对桁架屈曲分析结果的影响对比

    模态阶数 保留杆10单元 去除杆10单元
    屈曲因子 屈曲杆件 屈曲因子 屈曲杆件
    1 3.03×10-6 杆10 0.821 杆8
    2 1.21×10-5 杆10 0.898 杆3
    3 2.73×10-5 杆10 1.295 杆4
    4 4.87×10-5 杆10 2.929 杆5
    5 7.64×10-5 杆10 3.284 杆8
    6 1.11×10-4 杆10 3.590 杆3
    7 1.53×10-4 杆10 5.177 杆4
    8 2.02×10-4 杆10 7.390 杆8
    9 2.60×10-4 杆10 8.073 杆3
    10 3.69×10-4 杆10 11.643 杆4
    11 4.31×10-4 杆10 11.707 杆5
    12 5.32×10-4 杆10 13.154 杆8
    13 6.58×10-4 杆10 14.357 杆3
    14 8.09×10-4 杆10 20.618 杆8
    15 9.89×10-4 杆10 20.707 杆4
    16 1.20×10-3 杆10 22.481 杆3
    17 1.42×10-3 杆10 26.328 杆5
    18 1.63×10-3 杆10 29.869 杆8
    19 1.79×10-3 杆10 32.423 杆4
    20 1.84×10-3 杆10 32.526 杆3
    21 0.821 杆8 41.044 杆8
    22 0.898 杆3 44.629 杆3
    23 1.295 杆4 46.822 杆5
    24 2.929 杆5 46.910 杆4
    25 3.284 杆8 54.312 杆8
    26 3.590 杆3 58.946 杆3
    27 5.177 杆4 64.365 杆4
    28 7.390 杆8 69.622 杆8
    29 8.073 杆3 73.314 杆5
    30 11.643 杆4 75.343 杆3
    下载: 导出CSV

    表  3  十杆平面桁架优化结果

    杆件 截面积/cm2 截面半径/cm 轴向应力/MPa
    1 4.985 1.260 100.30
    2 4.993 1.261 100.14
    3 124.653 6.299 -8.02
    4 3.142 1.000 0
    5 3.142 1.000 0
    6 4.993 1.261 100.14
    7 7.113 1.505 99.41
    8 0 0 -
    9 0 0 -
    10 147.613 6.855 -4.79
    下载: 导出CSV

    表  4  十杆平面桁架优化后前十阶屈曲因子

    模态阶数 屈曲因子
    1 0.998
    2 1.006
    3 3.990
    4 4.021
    5 8.976
    6 9.040
    7 15.970
    8 16.070
    9 25.020
    10 25.150
    下载: 导出CSV
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  • 收稿日期:  2017-11-28
  • 刊出日期:  2019-01-05

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