非线性动力分析的广义精细积分法

Generalized precise time domain integration method for nonlinear dynamic analysis

针对非线性动力状态方程=H·v+f(v,t),结合广义精细积分法和预估-校正法,提出了用于非线性动力分析的广义精细积分法。在任一时间子域内,对计算过程中待求的vk+j/m(j=1,2,…,m),利用当前时刻的vk进行预估。将离散的非线性项用拉格朗日插值多项式展开并视为外荷载,结合广义精细积分法即可求解非线性系统的动力响应。该方法计算格式统一,易于编程,与四种单步法、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,该方法具有很高的精度、稳定性及较高的效率。可用于多自由度结构体系的非线性动力反应分析。

Aiming at the nonlinear dynamic state equation = H·v ＋ f（ v,t）,the generalized precise time domain integration method for nonlinear dynamic analysis was proposed using the generalized precise integration method combined with the predictor-correction one. Firstly,in any time-subdomain,the variable vkat the current time moment was used to pre-estimate the variable to be solved vk ＋ j/m（ j = 1,2,…,m） in the process of computation. Then the discrete nonlinear terms were expanded with Lagrange interpolation polynomial and taken as external loads,and the generalized precise integration method was used to directly solve the dynamic response of a nonlinear system. The proposed method was compared with four single-step methods,primary predictor-correction one and the predictor-corrector-symplectic time subdomain one. The numerical example results showed that the proposed method is easy to program and has a uniform computing format,higher accuracy,stability and efficiency; it can be applied in nonlinear dynamic response analysis of multi-DOF structural systems.