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PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
A Boundary Element Method Based Meshless Method for Buckling Analysis of Elastic Plates
B. Chinnaboon1, S. Chucheepsakul1 and J.T. Katsikadelis2
1Department 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", Civil-Comp 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.
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 boundary-domain 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  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.  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  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 BEM-based 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:
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