极坐标下薄板弯曲问题的重心有理插值法

doi:10.3976/j.issn.1002-4026.2016.02.015

Abstract

Abstract:

We apply barycentric rational interpolation collocation method (BRICM) to the bending problem of a thin plate in polar coordinates. It approximates an unknown function with barycentric rational interpolation by compelling a biharmonic equation to equal to the unknown function at discrete nodes, and acquires the discrete algebraic equations of the biharmonic equation. It further denotes the discrete algebraic equations as a matrix by the differential matrix of barycentric rational interpolation. It eventually solves the differential equations with a boundary conditions mixed replacement method. Numerical instances demonstrate that the method has simple calculation formulae for bending problem of a thin plate in polar coordinates, convenient program and high calculation precision.

Key words: polar coordinate, bending problem, barycentric rational interpolation method, biharmonic equation, boundary value problem

CLC Number:

O241

ZHUANG Meiling, WANG Zhaoqing,ZHANG Lei, JI Siyuan. Barycentric rational interpolation collocation method for bending problem of a thin plate in polar coordinates[J].SHANDONG SCIENCE, 2016, 29(2): 82-87.

References

［1］DESHMUKH K C, WARBHE S D, KULKARNI V S. Quasistatic thermal deflection of a thin clamped circular plate due to heat generation［J］. Journal of Thermal Stresses, 2009, 32(9):877-886.
［2］WANG Z Q, LI S C, Ping Y, et al. A highly accurate regular domain collocation method for solving potential problems in the irregular doubly connected domains［J］. Mathematical Problems in Engineering, 2014 (1):1-9.
［3］MOHYUDDIN S T, YILDIRIM A, HOSSEINI M M. An iterative algorithm for fifthorder boundary value problems［J］. World Applied Sciences Journal, 2010(5):531-535
［4］VIRDI K S. Finite difference method for nonliear analysis of structures［J］. Journal of Constructional Steel Research, 2006, 62(11): 1210-1218.
［5］KWON Y W, BANG H. The finite element method using MATLAB［M］. Boca Raton, FL, USA: CRC Press, Inc.1996.
［6］TANAKA M, MATSUMOTO T, OIDA S. A boundary element method applied to the elastostatic bending problem of beamstiffened plates［J］. Engineering Analysis with Boundary Elements, 2000, 24(10): 751-758.
［7］DONNING BM, LIU WK. Meshless methods for sheardeformable beams and plates［J］. Computer Methods in Applied Mechanics and Engineering, 1998, 152(1/2): 47-71.
［8］WANG X, BERT CW, STRIZ AG. Differential quadrature analysis of deflection,buckling,and free vibration of beams and rectangular plates［J］. Computers & Structures, 1993, 48(3): 473-479.
［9］SHAO W, WU X. Fourier differential quadrature method for irregular thin plate bending problems on Winkler foundation［J］. Engineering Analysis with Boundary Elements, 2011, 35(35):389-394.
［10］ROSTAMIYAN Y, FEREIDOON A, DAVOUDABADI M R， et al. Anzlytical approach to investigation of deflection of circular plate under uniforn load by homotopy load by homotopy perturbation method ［J］. Mathematical and Computational Applications, 2010, 15( 5):816-821.
［11］马燕, 王兆清, 唐炳涛. 波动问题的高精度重心有理插值配点法［J］. 山东科学, 2012, 25(3): 80-87.
［12］王兆清，綦甲帅，唐炳涛. 奇异源项问题的重心插值数值解［J］. 计算物理，2011，28(6): 883-888.
［13］綦甲帅，王兆清. 重心插值Galerkin法求解梁弯曲变形问题［J］. 山东科学，2013，26(3): 60-65.
［14］李树忱，王兆清. 高精度无网格重心插值配点法—算法、程序及工程应用［M］. 北京：科学出版社，2012.
［15］VENTSEL E, KRAUTHAMMER T. Thin plates and shells: Theory, Analysis and Applications ［M］. USA :CRC Press,2001.
［16］NG T Y, LI H,CHENG J Q, et al. A novel true meshless numerical technique (hMDOR method) for the deformation control of circular plates integrated with piezoelectric sensors/actuators［J］.Smart Materials & Structures, 2003, 12(6):955-961.

Metrics

Comments

Recommended 0

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), which permits third parties to freely share (i.e., copy and redistribute the material in any medium or format) and adapt (i.e., remix, transform, or build upon the material) the articles published in this journal, provided that appropriate credit is given, a link to the license is provided, and any changes made are indicated. The material may not be used for commercial purposes. For details of the CC BY-NC 4.0 license, please visit: https://creativecommons.org/licenses/by-nc/4.0

[1]	TANG Qiu-yun , WANG Ming-gao. Existence and uniqueness of positive solutions for boundary value problems integro-differential equations on infinite interval [J]. Shandong Science, 2020, 33(1): 124-130.
[2]	ZHOU Shilei,DONG Xue,DONG Xiaoyu. Existence and multiplicity of positive solutions of secondorder ordinary differential equations [J]. SHANDONG SCIENCE, 2015, 28(6): 116-120.
[3]	WU Xiang-Yun. Existence of symmetric solutions for a kind of second-order threepoint boundary value problem on a measure chain [J]. J4, 2014, 27(2): 98-101.
[4]	LU Hui-Qin, DU Fei-Yan. ontrivial solutions of fourthorder m-point resonance boundary value problem [J]. J4, 2013, 26(6): 5-8.
[5]	QI Jia-Shuai, WANG Zhao-Qing. The solution of beam bending problem with barycentric rational interpolation Galerkin method [J]. J4, 2013, 26(3): 60-65.
[6]	GUO Huan, HOU Wen-Ying, LU Hui-Qin. Existence of multiple solutions of a fourth-order three-point boundary value problem with a p-Laplacian operator [J]. J4, 2013, 26(1): 6-9.
[7]	WUXiang-Yun. Existence of positive solutions of a type of beam equation boundary value problems [J]. J4, 2012, 25(5): 6-10.
[8]	WANG Long, YAN Bao-Qiang. Research on the eigenvalues of nonlocal boundary value problems of a second-order linear differential equation [J]. Shandong Science, 2011, 24(6): 15-18.

Barycentric rational interpolation collocation method for bending problem of a thin plate in polar coordinates

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 8

Metrics

Comments

Recommended 0