Free vibration and buckling analysis of thin plates subjected to high gradients stresses using the combination of finite strip and boundary element methods

Abstract

Free vibration and buckling analysis of thin plates under arbitrary loading is investigated taking the advantages of both boundary element and finite strip methods. In the first step, the governing differential equation is converted to equivalent integral equation using static fundamental solutions of bi harmonic equation. Moreover, domain integrals due to inertia and in-plane forces are evaluated applying the finite strip interpolation functions to express the displacement field. This leads to a reduction of the size of the problem so that the mesh generation becomes easier and the computational efforts are reduced. In the buckling analysis, the near boundary stresses are calculated using a transformation method to cope with singularities. The proposed method can be easily applied to arbitrarily distributed and concentrated edge loading for different boundary conditions. The accuracy and efficiency of the presented method has been investigated through the solution of some sample problems for rectangular and skew plates.