能量一致积分方法是一种二阶精度、无条件稳定的逐步积分方法。为提高计算精度,将辛Runge-Kutta方法进行改进,构造出高阶能量一致积分方法一般形式。这种方法既保持了四阶精度,又具有能量一致属性。通过非线性弹性算例验证了方法的精度和数值稳定属性。将方法应用到桁架单元,推导了具体计算格式,并完成对应的非线性计算程序。程序集成了二阶与四阶能量一致积分方法、平均加速度方法(AAM)以及由AAM构造的四阶方法。通过弹性摆与平面桁架结构非线性动力分析,对比四种逐步积分方法。分析结果表明,四阶能量一致积分方法在精度、稳定性与计算效率上优于其它三种方法。
Abstract
The energy consistent integration method is a second-order and unconditionally stable step-by-step integration method. To improve the accuracy of this method, a symplectic Runge-Kutta method is improved to construct the general form of the high-order energy consistent integration method. This method maintains both fourth-order accuracy and energy consistency properties. The accuracy and numerical stability properties of the method are verified by a non-linearly elastic example. For the truss element, the specific application format of the new method is deduced, and the corresponding nonlinear program is completed. The program includes the second and fourth-order energy consistent integration methods, the average acceleration method (AAM) and the fourth-order method constructed from AAM. Four step-by-step integration methods were compared by nonlinear dynamic analysis of elastic pendulum and planar truss structures. The analysis results show that the fourth-order energy consistent integration method is better than the other three methods in terms of accuracy, stability and computational efficiency.
关键词
逐步积分方法 /
能量一致 /
非线性 /
数值稳定 /
平均加速度方法 /
辛方法
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Key words
step-by-step integration methods /
energy consistent /
nonlinearity /
numerical stability /
average acceleration method /
symplectic method
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