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功能梯度材料动力学问题的POD模型降阶分析

郑保敬 梁钰 高效伟 朱强华 吴泽艳

郑保敬, 梁钰, 高效伟, 朱强华, 吴泽艳. 功能梯度材料动力学问题的POD模型降阶分析[J]. 力学学报, 2018, 50(4): 787-797. doi: 10.6052/0459-1879-18-069
引用本文: 郑保敬, 梁钰, 高效伟, 朱强华, 吴泽艳. 功能梯度材料动力学问题的POD模型降阶分析[J]. 力学学报, 2018, 50(4): 787-797. doi: 10.6052/0459-1879-18-069
Zheng Baojing, Liang Yu, Gao Xiaowei, Zhu Qianghua, Wu Zeyan. ANALYSIS FOR DYNAMIC RESPONSE OF FUNCTIONALLY GRADED MATERIALS USING POD BASED REDUCED ORDER MODEL N[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 787-797. doi: 10.6052/0459-1879-18-069
Citation: Zheng Baojing, Liang Yu, Gao Xiaowei, Zhu Qianghua, Wu Zeyan. ANALYSIS FOR DYNAMIC RESPONSE OF FUNCTIONALLY GRADED MATERIALS USING POD BASED REDUCED ORDER MODEL N[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 787-797. doi: 10.6052/0459-1879-18-069

功能梯度材料动力学问题的POD模型降阶分析

doi: 10.6052/0459-1879-18-069
基金项目: 国家自然科学基金资助项目(11602129, 11672061).
详细信息
    作者简介:

    *郑保敬, 讲师, 主要研究方向: 计算固体力学 . E-mail: zheng _-bj@126. com

    通讯作者:

    郑保敬

  • 中图分类号: O321;

ANALYSIS FOR DYNAMIC RESPONSE OF FUNCTIONALLY GRADED MATERIALS USING POD BASED REDUCED ORDER MODEL N

  • 摘要: 为了快速分析非均质材料结构在复杂载荷作用下的动态响应, 提出一种模型降阶方法, 只需计算结构在简单均质材料情况下的动力学问题, 进而用其计算结果对非均质材料结构进行分析. 首先, 采用结构内部任意一点处的材料参数值作为整个结构的材料参数, 利用有限元分析软件计算该均质材料结构在动态载荷作用下的位移场建立数据库, 该数据库包含计算模型各个节点(自由度为L)在某时间段内L个时刻的位移; 其次, 对数据库中的信息按照时间离散的特定方式组集成瞬像矩阵, 并利用特征正交分解方法对其进行分解, 得到该模型的H个特征正交基底, 选取其中能反应模型主要特征的H<L?N个(其中~)作为一组最优基底, 通过这组基底建立模型的低阶离散控制方程; 最后, 求解低阶离散微分方程组, 得到功能梯度材料结构在复杂载荷作用下的位移场. 文中分别给出二维和三维算例, 比较了降阶模型和全阶模型计算结果, 验证了该方法的有效性, 并且计算效率能提高1 1)2个数量级.

     

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  • 刊出日期:  2018-07-18

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