A Calculation Method for Structural Dynamic Responses Based on the Approximation Theory of Radial Basis Function
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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.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.
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[1] 刘章军, 陈建兵. 结构动力学[M]. 北京: 中国水利水电出版社, 2012.(LIU Zhang-jun, CHEN Jian-bin.Structural Dynamics [M]. Beijing: China Water Conservancy and Hydropower Press, 2012.(in Chinese)) [2] Chopra A K.Dynamics of Structures:Theory and Applications to Earthquake Engineering[M]. 1993.(影印版. 第1版. 清华大学出版社, 2005). [3] 马利敏. 径向基函数逼近中的若干理论、方法及其应用[D]. 博士学位论文. 上海: 复旦大学, 2009.(MA Li-min. Some theory, methods and application in RBF approaching[D]. PhD Thesis. Shanghai: Fudan University, 2009.(in Chinese)) [4] 徐次达, 陈学潮, 郑瑞芬. 新计算力学加权残值法———原理、方法及应用[M]. 上海: 同济大学出版社, 1997.(XU Ci-da, CHEN Xue-chao, ZHENG Rui-fen.A New Computational Mechanics of Weighted Residual Method—Principle, Method and Application [M]. Shanghai: Tongji University Press, 1997.(in Chinese)) [5] 张雄, 刘岩. 无网格法[M]. 北京: 清华大学出版社, 2004.(ZHANG Xiong, LIU Yan.Meshless Method [M]. Beijing: Tsinghua University Press, 2004.(in Chinese)) [6] 刘桂荣, 顾元通. 无网格法理论及程序设计[M]. 王建明, 周学军 译. 济南: 山东大学出版社, 2007.(LIU Gui-rong, GU Yuan-tong.An Introduction to Meshfree Methods and Their Programming [M]. WANG Jian-ming, ZHOU Xue-jun transl. Jinan: Shandong University Press, 2007.(in Chinese)) [7] 吴宗敏. 径向基函数、散乱数据拟合与无网格偏微分方程数值解[J]. 工程数学学报, 2002,19(2): 1-12.(WU Zong-min. Radial basis function scattered data interpolation and the meshless method of numerical solution of PDEs[J].Journal of Engineering Mathematics,2002,19(2): 1-12.(in Chinese)) [8] 钟万勰. 应用力学的辛数学方法[M]. 北京: 高等教育出版社, 2006.(ZHONG Wan-xi.Symplectic Mathematics Method in Applied Mechanics [M]. Beijing: Higher Education Press, 2006.(in Chinese)) [9] 储德文. 结构动力响应的精细时程积分法研究[D]. 硕士学位论文. 北京: 北方交通大学, 2002.(CHU De-wen. Study on precise time interval integration method in structural dynamics response[D]. Master Thesis. Beijing: Northern Jiaotong University, 2002.(in Chinese))
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