摘要
提出将"时间间隔"替换"空间距离"作为径向基函数的自变量,利用径向基函数逼近的思想,结合加权余量配点法,用于结构动力响应的数值分析.并且针对结构动力学的特点,发展了位移、速度、加速度联合插值的径向基函数表达式,提出了精密计算的概念和标准.根据实际算例表明,该方法对比传统的Newmark法、Wilson-θ法、Runge-Kutta(龙格-库塔)法,在求解强刚性动力学方程,结构瞬态段的动力响应方面具有明显的优势,其计算精度与精细时程积分法相当.该方法与计算效率相关的动力特征矩阵,以及问题的自由度无关,因此针对大规模问题具有很好的适用性,是构建结构动力响应计算方法的新途径.
A newnumerical calculation method for structural dynamic responses was proposed based on the approximation theory of radial basis function( R BF) and weighted residual collocation point method, with the time interval to replace the space distance as the independent variable of R BF for the first time. Aimed at the numerical characteristics of structural dynamics,a newR BF expression of joint interpolation combining displacement,velocity and acceleration was developed,and the concept and standard for precise calculation put forward. According to the numerical examples,the newmethod has significant advantages in solving strong stiff dynamic equations and structural transient-phase dynamic responses,compared with the N ewmark method,W ilson-θ method and R unge-Kutta method. Its calculation accuracy is equivalent to that of the precise time-integration method. T his newcalculation method is independent of the computation efficiency-related dynamic eigen-matrix and the degrees of freedom of a problem. It has good applicability to some large-scale problems,and makes a promising way to the calculation of structural dynamic responses.
出处
《应用数学和力学》
CSCD
北大核心
2014年第5期533-541,共9页
Applied Mathematics and Mechanics
基金
重庆市教委科学技术研究项目(KJ100417)
关键词
径向基函数
加权余量配点法
结构动力学
精细时程积分法
radial basis function
w eighted residual collocation point method
structural dynamics
pre-cise time-integration method
