Open Access

ARTICLE

A Meshless Hybrid Boundary Node Method for Kirchhoff Plate Bending Problems

by F. Tan¹, Y.L. Zhang¹, Y.H. Wang³, Y. Miao³

1 State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China
2 Corresponding author, Tel: +86-15926324066; Fax: +86-27-87198805; Email: figotan@163.com
3 School of Civil Engineering and Mechanics, Huazhong University of Science and Technology,Wuhan 430074, China

Computer Modeling in Engineering & Sciences 2011, 75(1), 1-32. https://doi.org/10.3970/cmes.2011.075.001

Abstract

The meshless hybrid boundary node method (HBNM) for solving the bending problem of the Kirchhoff thin plate is presented and discussed in the present paper. In this method, the solution is divided into two parts, i.e. the complementary solution and the particular solution. The particular solution is approximated by the radial basis function (RBF) via dual reciprocity method (DRM), while the complementary one is solved by means of HBNM. The discrete equations of HBNM are obtained from a variational principle using a modified hybrid functional, in which the independent variables are the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain. The moving least squares (MLS) method is employed to approximate the boundary variables whereas the domain variables are interpolated by a linear combination of fundamental solutions of both the biharmonic equation and Laplace's equation. The present method is a truly boundary type meshless one as it does not require the `boundary element mesh', either for the purpose of interpolation of the variables or for the integration of `energy'. Several numerical examples are presented to illustrate the implementation and performance of the present method. It is shown that high accuracy can be achieved with a small node number for clamped and simply supported edge conditions.

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