Analytical Solution for Buckling of Annular Sectorial Porous Plates

In this article, an analytical solution for buckling of annular sectorial porous plates, is presented. At first, based on first order shear deformation plate theory, the governing equilibrium equations and boundary conditions are obtained using minimum total potential energy principle. Then, the stability equations of the plate, are derived in terms of infinitesimal displacements using adjacent equilibrium criterion. Since these equations are highly coupled, it is so difficult to find an analytical solution for them. So, by introducing four auxiliary functions and doing some mathematical manipulations, the stability equations are decoupled and converted to two independent differential equation which can be solved analytically. For this purpose, it has been assumed the simply supported boundary conditions for the radial edges and desired boundary conditions for the circumferential edges of the plate. Finally, the critical buckling load has been calculated for different conditions of the plate. In section of numerical results, the effect of different geometrical parameters, such as sector angle, thickness and inner radius of the plate, also effect of porosity of the plate upon the critical buckling load has been studied for different arbitrary boundary conditions on circumferential edges. The result show that the effect of increase in porosity of the plate upon decrease of the critical buckling load is significantly fewer than the effect of geometrical parameters and the boundary conditions.