Mesh-free radial basis function method for buckling analysis of non-uniformly loaded arbitrarily shaped shear deformable plates

A mesh-free radial basis function (RBF) method is employed for the buckling analysis of non-uniformly loaded thick plates. The field variables are approximated using a set of scattered nodes in the problem domain. The number of nodes and nodal distribution in the problem domain can be easily changed without a complex procedure for desired computational accuracy. The shape functions possess the 'partition of unity' properties. Based on the two-dimensional (2D) plane stress problem, a variational form of the static system of equations is formulated in terms of displacements, and is discretised. The initial (i.e., pre-buckling) stresses are obtained by solving the discrete system of equations. Based on the first-order shear deformation plate theory, a variational form of the plate problem with previously obtained initial stresses is established and discretised as the eigenvalue equation. The buckling loads of circular, trapezoidal and skew plates are presented. The present results have good convergence and are in good agreement with the finite element solutions. The present mesh-free radial basis function method is effective for the buckling analysis of non-uniformly loaded plates. © 2003 Elsevier B.V. All rights reserved.