Flexural vibration and buckling analysis of orthotropic plates by the boundary element method

A numerical solution technique by the boundary element method is developed in this paper for the flexural vibration and buckling analysis of elastic orthotropic plates according to Kirchhoff's theory. The integral formulations of the problem make use of the same fundamental solution as for the bending of orthotropic plates. An assumed unknown transverse distributed loading, defined inside the plate domain, is introduced for representing the inertia forces of vibration and the in-plane forces of buckling of the plate. The integral equations necessary for solving the problem of interest, are derived from the integral representations developed earlier for the bending analysis of orthotropic plates. A simple discretization scheme for the plate boundary and its interior domain is adopted in this paper for establishing the integral equations thus obtained in matrix form. After elimination of the conventional boundary unknowns, the flexural vibration or the buckling problem of an orthotropic plate is finally reduced into an eigenvalue problem of a square matrix. The eigenvalues and eigenvectors of that square matrix correspond respectively to the frequencies and the deflection mode shapes of the flexural vibration problem, or to the critical loads and the curvature mode shapes of the buckling problem. Several computational examples of vibration and buckling problems with various boundary conditions are presented, and the numerical results demonstrate, in comparison with some published results, a satisfactory accuracy of the proposed method.