用于非线性动力分析的一种高效精细积分单步法  

An efficient precise integration single-step method for nonlinear dynamic analysis

作　　者：王海波[1] 陈晋[1] 李少毅[1] 

机构地区：[1]中南大学土木工程学院,长沙410075

出　　处：《振动与冲击》2017年第15期158-162,229,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(50908230)

摘　　要：针对非线性动力状态方程v=H·v+f(v,t),结合精细积分法和Romberg数值积分,对计算过程中待求的v_(k+j/m)(j=1,2,…,m),利用当前时刻vk,通过二阶龙格库塔法进行预估,提出了一种避免状态矩阵求逆的高效精细积分单步法。该方法计算格式统一,易于编程,通过选取m值,可进行不同计算精度的计算。与两种单步法、一次预-校法及预估校正-辛时间子域法进行数值比较,计算结果表明,该方法具有高精度、高效率及较好的稳定性。在求解多自由度、强非线性动力响应问题中具有较大优势。Aiming at the state equation v= H · v + f( v,t) used for a nonlinear dynamic system,an efficient precise integration single-step method was proposed using a combination of the precise integration method and Romberg numerical integration. In the numerical integration process,the state matrix inversion was avoided and vkwas used to estimate the unknown v_(k + j/m)( j = 1,2,…m) with the two-order Runge-Kutta method. It was shown that the proposed algorithm with a uniform computing scheme is easy to be programmed; computations are performed with different accuracies through selecting the value of m. The numerical results showed that compared with two single-step methods,the predict-correct method and the predictor-corrector symplectic time-subdomain algorithm,the proposed method is more accurate,more efficient and more stable,it is more superior for solving dynamic response problems of multi-DOF systems and strongly nonlinear ones.

关 键 词：非线性动力方程 精细积分法 Romberg数值积分 龙格库塔法 单步法 

分 类 号：O322[理学—一般力学与力学基础] TU311.3[理学—力学]