A BEM-based meshless solution to buckling and vibration problems of orthotropicplates

In this paper a BEM-based meshless solution is presented to buckling and vibration problems of Kirchhoff orthotropic plates with arbitrary shape. The plate is subjected to compressive centrally applied load together with arbitrarily transverse distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting buckling and vibration problems are described by partial differential equations in terms of the deflection. Both problems are solved employing the Analog Equation Method (AEM). According to this method the fourth-order partial differential equation describing the response of the orthotropic plate is converted to an equivalent linear problem for an isotropic plate subjected only to a fictitious load under the same boundary conditions. The AEM is applied to the problem at hand as a boundary-only method by approximating the fictitious load with a radial basis function series. Thus, the method retains all the advantages of the pure BEM using a known simple fundamental solution. Example problems are presented for orthotropic plates, subjected to compressive or vibratory loading, to illustrate the method and demonstrate its efficiency and its accuracy.