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载荷作用位置不确定条件下结构动态稳健性拓扑优化设计

王栋

王栋. 载荷作用位置不确定条件下结构动态稳健性拓扑优化设计[J]. 力学学报, 2021, 53(5): 1439-1448. doi: 10.6052/0459-1879-21-009
引用本文: 王栋. 载荷作用位置不确定条件下结构动态稳健性拓扑优化设计[J]. 力学学报, 2021, 53(5): 1439-1448. doi: 10.6052/0459-1879-21-009
Wang Dong. ROBUST DYNAMIC TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURE SUBJECTED TO HARMONIC EXCITATION OF LOADING POSITION UNCERTAINTY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1439-1448. doi: 10.6052/0459-1879-21-009
Citation: Wang Dong. ROBUST DYNAMIC TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURE SUBJECTED TO HARMONIC EXCITATION OF LOADING POSITION UNCERTAINTY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1439-1448. doi: 10.6052/0459-1879-21-009

载荷作用位置不确定条件下结构动态稳健性拓扑优化设计

doi: 10.6052/0459-1879-21-009
基金项目: 1)国家自然科学基金(51975470);陕西省自然科学基础研究基金(2020JM-114)
详细信息
    作者简介:

    2)王栋, 教授, 主要研究方向: 结构力学行为分析与优化设计. E-mail: dwang@nwpu.edu.cn

    通讯作者:

    王栋

  • 中图分类号: O327

ROBUST DYNAMIC TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURE SUBJECTED TO HARMONIC EXCITATION OF LOADING POSITION UNCERTAINTY

  • 摘要: 研究当外载荷作用位置不确定时, 连续体结构动态稳健性拓扑优化设计. 在减小结构对简谐激励动响应的同时, 有效降低其对外载荷作用点随机扰动的敏感性. 首先基于非概率凸模型的方法, 将外激励作用位置的不确定性用有界区间变量表示. 其次通过对加载位置的导数分析, 获得了在激励位置扰动情况下结构动柔顺度的二阶泰勒展开式. 基于变密度方法, 推导出了动柔顺度对拓扑设计变量的一阶灵敏度显性表达式. 最后在材料体积约束下, 采用移动渐近优化算法并结合载荷扰动区间内灵敏度的最大绝对值, 对连续体结构进行动态稳健性拓扑优化设计, 并与传统载荷位置固定条件下的确定性优化结果进行对比, 充分展示考虑外激励作用位置扰动对结构拓扑构型设计及其动柔顺度变化的影响. 数值优化结果表明, 采用文中提出的方法所获得的结构动响应的稳健性更高, 能有效抵抗外激励作用位置的随机扰动. 只要少许增大材料的体积, 稳健性优化设计的动响应将在整个载荷扰动区域内优于确定性优化结果.

     

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出版历程
  • 收稿日期:  2021-01-06
  • 刊出日期:  2021-05-18

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