基于径向基函数逼近的结构动力响应计算方法

徐绩青; 李正良; 吴林键

doi:10.3879/j.issn.1000-0887.2014.05.007

基于径向基函数逼近的结构动力响应计算方法

doi: 10.3879/j.issn.1000-0887.2014.05.007

¹重庆交通大学国家内河航道整治工程技术研究中心,水利水运工程教育部重点实验室,重庆 400074;²重庆交通大学河海学院, 重庆 400074;³重庆大学土木工程学院, 重庆 400045

基金项目: 重庆市教委科学技术研究项目（KJ100417）

详细信息

作者简介:
徐绩青(1974—)，男，重庆人，博士(通讯作者. E-mail: plappk@sina.com).

中图分类号: TV312
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出版历程
- 收稿日期: 2014-03-07
- 修回日期: 2014-04-08
- 刊出日期: 2014-05-15

A Calculation Method for Structural Dynamic Responses Based on the Approximation Theory of Radial Basis Function

¹National Engineering Technology Research Center for Inland Waterway Regulation, Key Laboratory of Hydraulic & Waterway Engineering of the Ministry of Education, Chongqing Jiaotong University, Chongqing 400074, P.R.China;²School of River & Ocean Engineering, Chongqing Jiaotong University, Chongqing 400074, P.R.China;³College of Civil Engineering, Chongqing University, Chongqing 400045, P.R.China

摘要

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.
- 径向基函数 /
- 加权余量配点法 /
- 结构动力学 /
- 精细时程积分法
Abstract: A new numerical calculation method for structural dynamic responses was proposed based on the approximation theory of radial basis function (RBF) and weighted residual collocation point method, with the time interval to replace the space distance as the independent variable of RBF for the first time. Aimed at the numerical characteristics of structural dynamics, a new RBF 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 new method has significant advantages in solving strong stiff dynamic equations and structural transient-phase dynamic responses, compared with the Newmark method, Wilson-θ method and Runge-Kutta method. Its calculation accuracy is equivalent to that of the precise time-integration method. This new calculation 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.
- radial basis function /
- weighted residual collocation point method /
- structural dynamics /
- precise time-integration method

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参考文献(9)

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