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一种结构动力时程分析的积分求微方法

李鸿晶 梅雨辰 任永亮

李鸿晶, 梅雨辰, 任永亮. 一种结构动力时程分析的积分求微方法[J]. 力学学报, 2019, 51(5): 1507-1516. doi: 10.6052/0459-1879-19-105
引用本文: 李鸿晶, 梅雨辰, 任永亮. 一种结构动力时程分析的积分求微方法[J]. 力学学报, 2019, 51(5): 1507-1516. doi: 10.6052/0459-1879-19-105
Li Hongjing, Mei Yuchen, Ren Yongliang. AN INTEGRAL DIFFERENTIATION PROCEDURE FOR DYNAMIC TIME-HISTORY RESPONSE ANALYSIS OF STRUCTURES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1507-1516. doi: 10.6052/0459-1879-19-105
Citation: Li Hongjing, Mei Yuchen, Ren Yongliang. AN INTEGRAL DIFFERENTIATION PROCEDURE FOR DYNAMIC TIME-HISTORY RESPONSE ANALYSIS OF STRUCTURES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1507-1516. doi: 10.6052/0459-1879-19-105

一种结构动力时程分析的积分求微方法

doi: 10.6052/0459-1879-19-105
基金项目: 1)国家自然科学基金项目(51478222);高等学校博士学科点专项科研基金项目助(20123221110011)
详细信息
    通讯作者:

    李鸿晶

  • 中图分类号: O325

AN INTEGRAL DIFFERENTIATION PROCEDURE FOR DYNAMIC TIME-HISTORY RESPONSE ANALYSIS OF STRUCTURES

  • 摘要: 传统采用微分求积(differential quadrature,DQ)法求解动力问题时都是以位移响应作为基本未知量,而将速度响应和加速度响应表示为位移响应的加权和的形式.如此做法需要处理线性方程组或者矩阵方程(Sylvester方程)才能求得动力响应,导出的算法一般为有条件稳定算法.本文利用动力响应的Duhamel积分解,逆用DQ原理,提出了一种计算卷积的高精度显式算法.该算法可以逐时段地求解出动力时程响应,当各时段内DQ节点分布完全一致时,仅须进行一次Vandermonde矩阵求逆计算即可应用于各个时段,一次性获得时段内多个时刻的位移响应值,因而具有计算效率高的优点.通过分析动力方程积分格式,证明本文动力算法传递矩阵的谱半径恒等于1,因而该算法具有无条件稳定特性,且计算过程中不会产生数值耗散. 本文算法的数值精度取决于分析时段内布置的DQ节点数量$N$,具有$N-1$阶代数精度.实际操作时可以取10个甚至更多的DQ节点数,从而获得比较高的数值精度.

     

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出版历程
  • 收稿日期:  2019-04-26
  • 刊出日期:  2019-09-18

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