卷积型最小二乘法求解梁的动力学问题

doi:10.6052/1000-0879-12-225

力学与实践 ›› 2013, Vol. 35 ›› Issue (4): 53-55.DOI: 10.6052/1000-0879-12-225

卷积型最小二乘法求解梁的动力学问题

李永莉¹, 赵志岗², 杨华¹

1. 济南大学土木建筑学院, 济南250022;
2. 天津大学力学系, 天津300072

收稿日期:2012-05-31 修回日期:2013-01-18 出版日期:2013-08-08 发布日期:2013-08-26
通讯作者: 李永莉,讲师,硕士,主要研究结构的数值计算.E-mail:cealiyl@ujn.edu.cn

THE CALCULATION OF THE DYNAMIC PROBLEM OF A BEAM BY METHOD OF CONVOLUTION-TYPE LEAST SQUARES METHOD

LI Yongli¹, ZHAO Zhigang², YANG Hua¹

1. School of Civil Engineering and Architecture, Jinan University, Jinan 250022, China;
2. Department of Mechanics, Tianjin University, Tianjin 300072, China

Received:2012-05-31 Revised:2013-01-18 Online:2013-08-08 Published:2013-08-26

摘要/Abstract

摘要：

提出了卷积型最小二乘法,并用其计算了不同初始条件和不同边界条件下梁的动力学问题,算例表明,方法概念简单,计算方便,精度高,计算工作量少,卷积型最小二乘法是计算结构动力学问题的一种简单、高效的方法,试函数可以不满足边界条件.

关键词:

结构动力学|最小二乘法|卷积|梁|加权残值法

Abstract:

In the existing analytical cable elements, the temperature effects are considered, with the unstressed length being calculated according to the temperature variation first and being taken as the reference state for the static strain. Therefore, the temperature strain and the strain by the static loads have different reference states. Based on Irvine's work, a temperature effect correction for an analytical cable element is made to overcome this problem. An example shows the rationality of the correction.

Key words:

structure dynamics|least square method|convolution|beam|method of weighted residuals

中图分类号:

O342

李永莉, 赵志岗, 杨华. 卷积型最小二乘法求解梁的动力学问题[J]. 力学与实践, 2013, 35(4): 53-55.

LI Yongli, ZHAO Zhigang, YANG Hua. THE CALCULATION OF THE DYNAMIC PROBLEM OF A BEAM BY METHOD OF CONVOLUTION-TYPE LEAST SQUARES METHOD[J]. Mechanics in Engineering, 2013, 35(4): 53-55.

参考文献

1 Clough RW. Dynamics of Structure. New York: McGrawHill Book Co., 1975
2 Newmark NM. A method of computation for structural dynamics. ASCE J of Engineering Mechanics Division, 1959,85(3): 67-94
3 Bathe KJ, Wilson EL. Numerical Methods in Finite Element Analysis. New Jersey: Prentice-Hall, Inc.,1976
4 Mather NB, Marmo OA. On enhancement of accuracy in direct integration dynamic response problems. Earthquake Engineering and Structural Dynamics, 1991, 20(7): 699-703
5 Gurtin ME. Variational principles for linear elastodynamics. Avchive for Rational Mechanics and Analysis, 1964,16(1): 34-50
6 罗恩. 关于线弹性动力学中各种Gurtin 型变分原理. 中国科学,A 辑,1987, 9: 936-948 (Luo En. On the Gurtin variational principles for linear elastodynamic. Science in China,Series A,1987, 9: 936-948 (in Chinese))
7 刘铁林, 陈海滨. 一种基于Gurtin 变分原理的非时间步参数逐步积分法. 沈阳建筑大学学报,2006,26(1): 11-14 (Liu Tielin, Chen Haibin. Step-by-step integration method of nontime-step parameter based on Gurtin variational principle. Journal of Shenyang Jianzhu University, 2006, 26(1): 11-14 (in Chinese))
8 宋立娜, 李勇军. 一种基于位移型Gurtin 变分原理的逐步积分法. 辽宁工学院学报, 2006,26(1): 56-59 (Song Lina, Li Yongjun. Step-by-step integration method based on Gurtin variational principle of displacement model. Journal of Liaoning Institute of Technology, 2006, 26(1): 56-59 (in Chinese))
9 彭建设, 杨杰, 袁玉全等. 矩形薄板瞬态响应的卷积型DQ 半解析法. 应用数学和力学,2009, 30(9):1065-1077 (Peng Jianshe, Yang Jie, Yuan Yuquan. Convolution-type semianalytic DQ approach for transient response of rectangular plates. Applied Mathematics and Mechanics, 2009, 30(9):1065-1077 (in Chinese))
10 毕继红, 郭淑卿. 应用Gurtin 变分原理求解板动力问题的样条有限元法. 天津城市建设学院学报,2000, 6(2):84-88 (Bi Jihong, Guo Shuqing. A spline ˉnite elenent methods for initial value problems of elastradynamics of plate with Gurtin variational principle. Journal of Tianjin Institute of Urban Construction, 2000, 6(2):84-88 (in Chinese))
11 徐次达, 陈学潮, 郑瑞芬. 新计算力学加权残值|| 原理、方法及应用. 上海: 同济大学出版社,1997
12 李永莉, 赵志岗. 用卷积型加权残值法求解梁的动力学问题. 力学与实践,2002, 24(2):47-49 (Li Yongli,Zhao Zhigang. The calculation for the dynamic problem of a beam by method of convolution-type weighed residuals. Mechanics in Engineering, 2002, 24(2):47-49 (in Chinese))
13 李永莉, 赵志岗, 侯志奎. 卷积型加权残值法求解薄壳的动力学问题. 力学与实践,2006, 28(3):71-73 (Li Yongli, Zhao Zhigang, Hou Zhikui. The thin shell solved by method of convolution-type weighted residuals. Mechanics in Engineering, 2006, 28(3):71-73 (in Chinese))
14 李永莉, 赵志岗, 侯志奎. 卷积型加权残值法求解薄板的动力学问题. 工程力学,2006, 23(1):43-46 (Li Yongli, Zhao Zhigang, Hou Zhikui. Dynamic analysis of thin plates by convolution-type weighted residuals method. Engineering Mechanics, 2006, 23(1):43-46 (in Chinese))
15 李永莉, 赵志岗, 侯志奎. 卷积型伽辽金法求解任意边界梁的动力学问题. 力学与实践,2008, 30(6):28-30 (Li Yongli, Zhao Zhigang, Hou Zhikui. The calculation of the dymamic problem of a beam with arbitrary boundary conditions by method of convolution-type Galerkin method. Mechanics in Engineering, 2008, 30(6):28-30 (in Chinese))

[1]	汪珍, 舒开鸥. 静定结构受力分析中约束力换算公式与二力杆的妙用¹⁾[J]. 力学与实践, 2020, 42(4): 511-515.
[2]	田振国. 结构力学教学中的几个问题¹⁾[J]. 力学与实践, 2019, 41(6): 728-732.
[3]	陈玲俐, 赵晓昱. 基于经典层合板理论的简支梁力学分析¹⁾[J]. 力学与实践, 2019, 41(2): 152-156.
[4]	郑玉国, 王瑜, 宋英梁. 刚度分配图乘法的基本原理及应用¹⁾[J]. 力学与实践, 2019, 41(2): 227-232.
[5]	孙旭峰. 结构力学中的换铰法应用刍议¹⁾[J]. 力学与实践, 2019, 41(1): 91-94.
[6]	周嘉舜, 王璠, 欧姸君, 黄世清, 何陵辉, 匡友弟. 计算杆件结构的自由度¹⁾[J]. 力学与实践, 2019, 41(1): 95-98.
[7]	朱俊儿. 从一个简单实验谈结构力学之美[J]. 力学与实践, 2018, 40(6): 723-726.
[8]	叶康生, 殷振炜. 欧拉梁弹性稳定分析的有限元p型超收敛算法¹⁾[J]. 力学与实践, 2018, 40(6): 647-652.
[9]	李振勇, 严新军, 陈国新, 刘鑫焱, 胡洪浩. 一种求解静定组合结构与桁架结构影响线的简便算法¹⁾[J]. 力学与实践, 2018, 40(5): 563-568.
[10]	孙宏杨, 邢沁妍. 基于结构力学求解器的框架“强柱弱梁”机制探讨¹⁾[J]. 力学与实践, 2018, 40(5): 569-573.
[11]	周克民. 结构拓扑优化的一些基本概念和研究方法¹⁾[J]. 力学与实践, 2018, 40(3): 245-252.
[12]	贾红英, 赵均海, 单建. “感而遂通”参与式教学法¹⁾——在结构力学课程中的探索与实践[J]. 力学与实践, 2018, 40(2): 222-225.
[13]	王崇安, 邢沁妍. 笛沙格定理的结构力学分析再证明[J]. 力学与实践, 2018, 40(2): 210-213.
[14]	刘胜来. 变刚度梁挠度曲线的Green函数法求解[J]. 力学与实践, 2017, 39(5): 445-448,444.
[15]	李明, 钟豪. 半结构法在中心对称结构计算中的应用[J]. 力学与实践, 2017, 39(4): 400-403.

卷积型最小二乘法求解梁的动力学问题

THE CALCULATION OF THE DYNAMIC PROBLEM OF A BEAM BY METHOD OF CONVOLUTION-TYPE LEAST SQUARES METHOD

PDF (PC)

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价