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CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 173
A Boundary Element Method Based Meshless Method for Buckling Analysis of Elastic Plates B. Chinnaboon^{1}, S. Chucheepsakul^{1} and J.T. Katsikadelis^{2}
^{1}Department of Civil Engineering, King Mongkut's University of Technology Thonburi, Bangkok, Thailand
B. Chinnaboon, S. Chucheepsakul, J.T. Katsikadelis, "A Boundary Element Method Based Meshless Method for Buckling Analysis of Elastic Plates", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 173, 2006. doi:10.4203/ccp.83.173
Keywords: boundary element method, meshless, buckling, analog equation method, elastic plates, radial basis functions, thin plate splines.
Summary
Buckling or elastic instability of plates is of great practical importance. Analytical
solutions of a plate buckling have been found in the simplest cases of support and
loading conditions. Numerical methods such as the finite element method have been
used by many researchers to investigate the buckling problems. More recently, the
boundary element method (BEM) has proved to be a powerful solver for the
plate buckling problems. In the early development of the BEM [1,2,3,4,5], domain integrals containing
domain curvature terms arise in the formulations which usually result in a combined
boundarydomain solution of the problem. Afterwards, the effort to overcome this
limitation has been made by using the concept of the dual reciprocity method. Elzein
and Syngellakis [6] have proposed two models for the plate deflection. The accuracy
of the results depends on the order of the Fourier approximation or the choice of
deflection functions. Lin et al. [7] have proposed the boundary integral formulation
which was in terms of three displacements of the plate's middle surface and the
planar loading and, or displacements applied at the boundary of the plate. A Fourier
series was also applied in their formulations. Recently, Neranzaki and Katsikadelis [8]
have proposed an analog equation method (AEM) for buckling of plates with
variable thickness. The AEM has been successfully employed to solve the plate
buckling problems without the limitations on the plate geometry, thickness variation and the
support and loading conditions. However, there are still domain integrals in the
formulations.
In this paper a BEMbased meshless method is developed for buckling analysis of elastic plates. The presented method was achieved using the concept of the analog equation method (AEM). According to this method the original eigenvalue problem for a governing differential equation of buckling is replaced by an equivalent problem for plate bending problem subjected to an "appropriate" fictitious load under the same boundary conditions. The domain integral caused by the fictitious load is approximated by using thin plate splines (TPSs) as a radial basis function series and then converted also to a line integral on the boundary using a technique based on the BEM. The formulation has no limitations on plate shape, and transverse and inplane boundary conditions. The eigenmodes of the actual problem are obtained from the known integral representation of the solution for the classical plate bending problem, which is derived using the fundamental solution of the biharmonic equation. The following conclusions can be drawn from this study:
References
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