AN ENHANCED ANALYTICAL MODEL FOR BUCKLING INVESTIGATION OF MINDLIN PLATES

Buckling analysis of isotropic, rectangular plates subjected to uniformly axial and biaxial and pure shear loads is presented in this paper. In order to take into account the effect of transverse shear deformation, the Mindlin first order shear theory has been applied to the plate’s analysis. The novelty of the paper is that, assuming that the solution is separable, a closed-form solution is developed by an extended Kantorovich method without any use of approximation for the boundary conditions. A range of numerical applications is described for isotropic plates of thin, moderately thick and thick geometry. The good agreement of the results obtained using the proposed method, compared to other published results achieved by other numerical approaches and analytical solutions available in literature, illustrates the applicability, the effectiveness and the accuracy of the method. 1 INTRODUCTION Motivated by the great interest in numerous engineering applications, buckling of twodimensional systems has been extensively investigated in literature. The simplest model adopted in literature for the analysis of thin plates is based on the classical Kirchhoff thin plate theory [1] and extensive analysis for elastic stability of plates based on analytical [2] or numerical [3] solutions of the Kirchhoff equation have been carried out. However, because the Kirchhoff model neglects the effects of transverse shear deformations, it can underestimates deflection and overestimates the buckling loads when such effects are significant, and a more refined model may be necessary. For moderately thick plates, models based on Mindlin plate theory [4] are usually very satisfactory, and elastic stability of rectangular plates has been largely studied and – due to the difficulties encountered to analytically solve the governing equilibrium equation – several semianalytical or numerical approaches has been proposed in literature. For its generality, the numerical analyses based on the finite element method are the most commonly used in handling buckling problems of structure with general geometry and boundary conditions [5]. Boundary element method [6], least squares-based finite difference method [7], finite strip method [8], are some of the alternative methods available in literature for the buckling analysis of Mindlin plates. When the geometry of the structure is sufficiently regular, ad-hoc, more efficient semianalytical techniques can be successfully adopted, and the obtained solution are often very useful for