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Review on precise time integration method and its derived formats[J].计算力学学报,2019,36(1):132~137

Review on precise time integration method and its derived formats
Review on precise time integration method and its derived formats

DOI：10.7511/jslx20170926002

 作者 单位 E-mail 吴杰 江苏科技大学 船舶与海洋工程学院, 镇江 212003 stephenwu@163.com 王志东 江苏科技大学 船舶与海洋工程学院, 镇江 212003 虞志浩 南京航空航天大学 直升机旋翼动力学国家级重点实验室, 南京 210016

旋翼气动弹性耦合动力学方程本质上是一组刚性比较大的非线性偏微分方程。在有限元结构离散后，可改写为非齐次微分方程组，其中非齐次项是桨叶运动量（位移与速度）和气动载荷的函数。针对这类方程，本文尝试引入精细积分法及其衍生格式，借助数值方法计算Duhamel积分项。从积分精度与数值稳定性方面比较研究具有代表性的精细库塔法和高精度直接积分法。结合隐式积分算法，评估精细积分法应用于旋翼动力学方程的可行性。算例表明，精细积分法对矩形直桨叶动力学方程具有足够的求解精度。

Helicopter rotor aeroelasticity is essentially described by a set of stiff and nonlinear partial differential equations.They can be rewritten as non-homogeneous ordinary differential equations after discretion by finite element method.The non-homogeneous terms depend on time response and aerodynamic loads of the blades.This paper introduces a precise time integration method (PTI) and its derived formats to solve this kind of equations.The Duhamel integration term in the derived formats can be calculated using this numerical method.It also selects and compares the precise-Kutta method and high precision direct scheme (HPD) on integration precision and numerical stability.At last,an implicit integration method is used to comprehensively evaluate PTI on rotor dynamics.Numerical examples indicate that HPD scheme is precise evough to be used for rectangular blades.