摘要
本文在[1]基础上提供了一类预测-校正积分模式,这种积分模式对具有对角质量阵的非线性动力学方程积分,无需求解高阶线性代数方程组,因而可以显著地提高计算效率与经济性,文中采用数值试验的方法讨论了预测-校正积分的非线性稳定性与精度;还介绍了一种判别复杂非线性问题的数值结果可信与否的简单办法;最后分析了一个大型工程实例——重载列车纵向动力学问题,计算结果与试验结果吻合很好。
Based on the Newmark's implicit integration algorithm which is well known and wide used in the domain of structural dynamic analyses, an explicit algorithm is constructed to form a predictor-corrector integration scheme. This scheme is not only simple but also with higher accuracy. By means of this predictor-corrector scheme,it is convenient to analyse complex nonlinear dynamic systems discrcted by finite element methods because of the needlessness of solving high order algebraic linear equations in each integration step.In this paper, the nonlinear numerical stability and accuracy of this scheme is discussed by using numerical experiment methods. It is shown that this predictor-corrector integration scheme may have higher accuracy than the Newmark (β = 1/4), Park and Houbolt methods as long as its stable condition is kept. A criterion is also presented in this paper to examine whether the calculation result is believable for complex nonlinear problem. At the end of this paper, an applied example of engineering problems is given.
