土石坝动力分析的改进二次加速度积分法
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摘要
土石坝动力分析常用的是Wilson-θ积分方法,但该方法用于分析高频问题和大步长问题时精度较低。针对该缺点提出一种改进的二次加速度积分法,该算法与一步二次加速度积分法相比,计算精度不变、稳定性要求容易满足,计算用时大大减少。对算法的基本原理、稳定性及精度进行了分析,并给出一个土石坝动力分析的算例,验证了该算法的可行性。与常用的Wilson-θ法、Newmark法和中心差分法进行了数值比较。计算结果表明:该算法在分析高频问题和大步长问题时,计算精度较高。
As a commonly used dynamic integration analysis method of earth-rock dam,Wilson-θ method has comparatively low accuracy in analyzing problems involving high frequency and long time interval.Aiming at the disadvantages,an improved quadratic acceleration integration method is put forward.Compared with the one step quadratic acceleration integration method,its numerical accuracy remains the same and the requirements of stability are more easily satisfied but the time needed in calculation is reduced sharply.And then,the fundamental,stability and accuracy of the method are analyzed.Moreover,a case study about the earth-rock dam dynamic analysis is given to prove the feasibility of the method.At last,by comparing the results of the proposed method with those of Wilson-θ method,Newmark method and Central difference method,the numerical accuracy has been analyzed.The results indicate that the proposed method is highly accurate in analyzing problems especially in high frequency and long time interval.
As a commonly used dynamic integration analysis method of earth-rock dam,Wilson-θ method has comparatively low accuracy in analyzing problems involving high frequency and long time interval.Aiming at the disadvantages,an improved quadratic acceleration integration method is put forward.Compared with the one step quadratic acceleration integration method,its numerical accuracy remains the same and the requirements of stability are more easily satisfied but the time needed in calculation is reduced sharply.And then,the fundamental,stability and accuracy of the method are analyzed.Moreover,a case study about the earth-rock dam dynamic analysis is given to prove the feasibility of the method.At last,by comparing the results of the proposed method with those of Wilson-θ method,Newmark method and Central difference method,the numerical accuracy has been analyzed.The results indicate that the proposed method is highly accurate in analyzing problems especially in high frequency and long time interval.
引文
[1]于建华,谢用九,魏泳涛.高等结构动力学[M].成都:四川大学出版社,2001.
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[2]宋又廉.基于三次样条插值的采样数据光滑曲线形成法[J].数据采集与处理,1999,14(2):193-196.SONG You-lian.Smooth curve output for dynamic process sampling data based on cubic polynomial interpolation[J].Journal of Data Acquisition&Processing,1999,14(2):193-196.
[3]钟万勰.单点子域积分与差分[J].力学学报,1996,28(2):159-163.ZHONG Wan-xie.Single point subdomain precise integration and finite difference[J].Chinese Journal of Theoretical and Applied Mechanics,1996,28(2):59-163.
[4]钟万勰.子域精细积分及偏微分方程的数值解[J].计算结构力学及其应用,1995,12(3):253-260.ZHONG Wan-xie.Subdomain precise integration method and numerical solution of partial differential equations[J].Computational Structural Mechanics and Applications,1995,12(3):253-260.
[5]孙焕纯.非线性结构动力分析的改进θ法[J].力学学报,1981,(2):153-164.SUN Huan-chun.An improved-θmethod for non-linear structural dynamic analysis[J].Chinese Journal of Theoretical and Applied Mechanics,1981,(2):153-164.
[6]张文飞.精确二次加速度的逐步积分法[J].大庆石油学院学报,1992,16(3):37-42.ZHANG Wen-fei.An accurate second order acceleration algorithm of step-by-step integration[J].Journal of Daqing Petroleum Institute,1992,16(3):37-42.
[7]BATHE K J,WILSON E L.Stability and accuracy analysis of direct integration methods[J].Earthquake Engineering and Structural Dynamics,1973,(1):283-291.
[8]HILBER H M,HUGHES T J R,TAYLOR R L.Improved numerical dissipation for time integration algorithms in structural dynamics[J].Earthquake Engineering and Structural Dynamics,1977,(5):283-292.
[9]HILBER H M,HUGHES T J R.Collocation dissipation and‘overshoot'for time integration schemes in structural dynamics[J].Earthquake Engineering and Structural Dynamics,1978,(6):99-118.
[10]顾淦臣.土石坝地震工程[M].南京:河海大学出版社,1989.
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