A non-discrete approach for analysis of plates with multiple subdomains

This paper presents a non-discrete approach for vibration and buckling analysis of rectangular Kirchhoff plates with mixed edge support conditions. A plate is decomposed into multiple rectangular subdomains along the change of the discontinuous support conditions. A dominant subdomain is established, whose Ritz coefficients in the displacement trial function are incorporated into the neighbouring subdomains, by imposing compatibility conditions for transverse displacement and slope along the non-discretized interconnecting boundaries. The automated Ritz method is employed to derive governing eigenvalue equations for the vibration and buckling analysis of the plate problem. The validity and accuracy of the proposed method are verified with convergence and comparison studies. Numerical results are presented for vibration and buckling of several selected rectangular plates with various combinations of mixed edge support conditions.