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结构优化半解析灵敏度及误差修正改进算法

张力丹 张盛 陈飙松 李云鹏

张力丹, 张盛, 陈飙松, 李云鹏. 结构优化半解析灵敏度及误差修正改进算法[J]. 力学学报, 2018, 50(4): 949-960. doi: 10.6052/0459-1879-18-058
引用本文: 张力丹, 张盛, 陈飙松, 李云鹏. 结构优化半解析灵敏度及误差修正改进算法[J]. 力学学报, 2018, 50(4): 949-960. doi: 10.6052/0459-1879-18-058
Zhang Lidan, Zhang Sheng, Chen Biaosong, Li Yunpeng. MODIFIED SEMI-ANALYTICAL SENSITIVITY ANALYSIS AND ITS ERROR CORRECTION TECHNIQUES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 949-960. doi: 10.6052/0459-1879-18-058
Citation: Zhang Lidan, Zhang Sheng, Chen Biaosong, Li Yunpeng. MODIFIED SEMI-ANALYTICAL SENSITIVITY ANALYSIS AND ITS ERROR CORRECTION TECHNIQUES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 949-960. doi: 10.6052/0459-1879-18-058

结构优化半解析灵敏度及误差修正改进算法

doi: 10.6052/0459-1879-18-058
基金项目: 国家重点研发计划(2016YFB0201602)和国家自然科学基金(11372064)资助项目.
详细信息
    通讯作者:

    陈飙松

  • 中图分类号: TB12;

MODIFIED SEMI-ANALYTICAL SENSITIVITY ANALYSIS AND ITS ERROR CORRECTION TECHNIQUES

  • 摘要: 提出结构半解析灵敏度分析及其针对刚体位移的误差修正方法的改进算法, 构建灵敏度分析与误差修正项可分离形式. 该方法实现简便, 数值精度不受摄动步长与单元数目的影响. 首先从总体角度推得静力问题的误差修正半解析灵敏度分析方法, 提出了位移误差修正灵敏度列式, 并给出算法实施途径; 然后将此思路推广于自振频率、屈曲临界载荷问题, 提出了相应的计算步骤. 随后, 给出梁单元与壳单元误差修正项的具体推导方法, 并分别使用两种单元构建有限元模型进行算例测试. 结果表明, 该方法适用于多种分析类型, 数值精度不受单元数目与摄动步长的影响. 由于灵敏度分析与误差修正项可以分开计算, 该方法支持将误差修正项直接叠加于灵敏度求解结果进行误差修正, 使已有灵敏度分析程序得到充分利用. 尤其对于复杂工程结构的优化设计, 特别是形状优化设计以及尺寸、形状混合优化设计, 相比于原误差修正方法, 实现更为简便, 效率有所提升, 能为半解析灵敏度分析方法及其程序实现提供新的思路.

     

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  • 刊出日期:  2018-07-18

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