The stability analysis of a rectangular plate supported at points of the corners

Abstract

The stability problem of a rectangular plate supported at points of corners under uniform pressures in its median plane is studied by using the reciprocal theorem. At first, according to the differential equation of transversal buckling displacement function for a thin rectangular plate, dual trigonometric series, and the reciprocal theorem, the equation of the deflection surface for a rectangular plate with four simple supported edges under uniform pressures in its median plane and a transversal concentrated unit load is established. Secondly, using the reciprocal theorem, the buckling equation for a rectangular plate supported at points of corners is derived. The unknowns here can be determined by the boundary conditions. The exact solution of critical load is given. Finally, as an example, a square plate has been calculated. The results show that the method is accurate and effective to solve the stability problem of rectangular plates. It can serve as technical reference for engineering designs.