Radial Basis Functions Methods for Strongly Nonlinear Beam

doi:10.3969/j.issn.1674-0696.2018.12.09

Journal of Chongqing Jiaotong University(Natural Science) ›› 2018, Vol. 37 ›› Issue (12): 55-60.DOI: 10.3969/j.issn.1674-0696.2018.12.09

• Port & Waterway · Hydraulic & Hydroelectric · Resources & Environment • Previous Articles Next Articles

Radial Basis Functions Methods for Strongly Nonlinear Beam

ZU Fuxing1, 2, XU Jiqing1, 2, LI Yanting1, 2

(1. National Inland Waterway Regulation Engineering Research Center, Chongqing Jiaotong University, Chongqing 400074, P. R. China; 2. Key Laboratory of Hydraulic & Waterway Engineering of the Ministry of Education, Chongqing Jiaotong University, Chongqing 400074, P. R. China)

Received:2018-01-25 Revised:2018-07-29 Online:2018-12-09 Published:2020-07-10

强非线性梁求解的径向基函数方法

祖福兴1,2，徐绩青1,2，李岩汀1,2

(1. 重庆交通大学国家内河航道整治工程技术研究中心，重庆 400074； 2. 重庆交通大学水利水运工程教育部重点实验室，重庆 400074)

作者简介:祖福兴(1973—)，男，福建龙岩人，博士研究生，主要从事港口、海岸及近海工程方面的研究。E-mail: zufuxing@126.com。通信作者：徐绩青(1974—)，男，山西夏县人，博士，主要从事计算力学，港口、海岸及近海工程方面的研究。E-mail: plappk@sina.com。18996470720
基金资助:
国家自然科学基金项目(51479015)；重庆市教委科学技术研究项目(KJ100417)

Abstract

Abstract: The idea of Radial Basis Functions (RBFs) approximation and the method of weighted residual collocation were combined to solve strongly nonlinear beams. And for different boundary conditions problems, the corresponding RBFs interpolation functions were proposed to decrease the numerical oscillation. By using proper compactness positive definite RBFs, a better solution could be obtained. The actual examples demonstrate that the proposed method has high calculation accuracy that the modified wavelet-Galerkin method and the numerical integration algorithm of the symplectic-conservative and energy-preserving method can achieve. Therefore, the proposed method provides a new way to solve the strongly nonlinear beam because of the simpler calculation process of collocation method than integration method.

Key words: port and waterway engineering, strong nonlinear beam, large deflection bending, meshless method

摘要： 针对强非线性梁提出了一种径向基函数逼近思想结合加权余量配点的求解方法；为减小数值震荡，针对不同问题的边值条件，提出了对应的径向基函数插值表达式，且采用适当的紧支撑正定径向基函数，可获得较好的求解效果。实际算例表明：方法计算精度高，可以达到修正小波伽辽金法、保辛-保能的数值积分法的计算效果；由于配点法相比积分法的计算过程更为简单，方法为强非线性梁的求解提出了一种新途径。

关键词: 港口航道工程, 强非线性梁, 大挠度弯曲, 无网格法

CLC Number:

ZU Fuxing1, 2, XU Jiqing1, 2, LI Yanting1, 2. Radial Basis Functions Methods for Strongly Nonlinear Beam[J]. Journal of Chongqing Jiaotong University(Natural Science), 2018, 37(12): 55-60.

祖福兴1,2，徐绩青1,2，李岩汀1,2. 强非线性梁求解的径向基函数方法[J]. 重庆交通大学学报（自然科学版）, 2018, 37(12): 55-60.

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Radial Basis Functions Methods for Strongly Nonlinear Beam

强非线性梁求解的径向基函数方法

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