[1]黄庆丰.一种改进的Wilson-θ法及其计算稳定性[J].华侨大学学报(自然科学版),2010,31(2):205-209.[doi:10.11830/ISSN.1000-5013.2010.02.0205]
　HUANG Qing-feng.An Improved Wilson-θ Method and Its Calculation Stability[J].Journal of Huaqiao University(Natural Science),2010,31(2):205-209.[doi:10.11830/ISSN.1000-5013.2010.02.0205]
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一种改进的Wilson-θ法及其计算稳定性()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第31卷
期数:
2010年第2期
页码:
205-209
栏目:
出版日期:
2010-03-20

文章信息/Info

Title:
An Improved Wilson-θ Method and Its Calculation Stability
文章编号:
1000-5013(2010)02-0205-05
作者:
黄庆丰
华侨大学土木工程学院
Author(s):
HUANG Qing-feng
College of Civil Engineering, Huaqiao University, Quanzhou 362021, China
关键词:
Wilson-θ法;  修正计算;  平衡方程;  附加运动;  约束条件
Keywords:
Wilsion-θ method;  modified computation;  dynamic equation;  additional motion;  constraint condition
分类号:
O302
DOI:
10.11830/ISSN.1000-5013.2010.02.0205
文献标志码:
A
摘要:
考虑系统计算运动参数的协调,运用系统的动力平衡改进Wilson-θ法积分.近似认为时间步长内,系统平衡方程与Wilson-θ法计算假定附加的系统运动约束条件的不协调程度不变,时间步长内产生的不平衡计算加速度,分量将为常量,由此导出时间步长终点的系统修正位移、速度和加速度计算式.结果表明,改进算法保留了Wilson-θ法在θ≥1.37时的无条件计算稳定性.算例结果显示,当时间步长取0.28 s时,改进算法减少约85%的相对误差,且明显减小了Wilson-θ法的超越现象.
Abstract:
An improved Wilsion-θ method is proposed for step-by-step integral on dynamic equation.It is assumed that the non-coordination degree is unchanged between the dynamic equation of system and the additional kinematic constraint condition given by calculation hypothesis of Wilsion-θ method,so the nonequilibrium component of calculation acceleration would be a constant,thereby,the revised formula is educed to calculate the displacement,velocity and acceleration of system at the end of time step.The unconditional stability of Wilsion-θ method for θ≥1.37 is preserved in the improved method,and examples show that,for 0.28 second time step,the improved method decreases the error of Wilson-θ method by about 85%,and the transcend of Wilsion-θ method is eliminated greatly.

参考文献/References:

[1] BATHE K J, WILSON E L. Numerical methods in finite analysis [M]. Englewood Cliffs, New Jersey:Prentice-Hall, Inc, 1976.
[2] 俞载道. 结构动力学基础 [M]. 上海:同济大学出版社, 1987.
[3] CLOUGH R W, PENZIEN J. Dynamics of structures [M]. New York:mcgraw-hill Book Company, inc, 1975.
[4] 黄庆丰, 王全凤. Wilson-θ法时程积分的运动约束和计算扰动 [J]. 计算力学学报, 2005(4):477-481.doi:10.3969/j.issn.1007-4708.2005.04.017.
[5] 黄庆丰, 王全凤, 胡云昌. 时程积分过程中的结构运动参数协调 [J]. 固体力学学报, 2004(1):7-10.doi:10.3969/j.issn.0254-7805.2004.01.002.
[6] 秦荣. 计算结构力学 [M]. 北京:科学出版社, 2001.

备注/Memo

备注/Memo:
国家自然科学基金资助项目(10872072); 华侨大学高层次人才科研启动项目(05BS305)
更新日期/Last Update: 2014-03-23