ABSTRACT
In most practical applications of thin plates the magnitude of the stresses acting on the surface parallel to the middle plane are small compared to the bending and membrane stresses. Since the plate is thin, this implies that the tractions on any surface parallel to the midplane are relatively small. In particular, an approximate state of plane stress exists. Plate buckling occurs only under large inplane loads. Stability analysis must include the effect of inplane forces on plate bending. Critical load is sought which causes an infinitesimally small shift in the equilibrium position. In classical stability theory this is referred to as the "adjacent equilibrium method." The proper boundary conditions are those which are sufficient to guarantee unique solutions to the governing equations. By applying energy principles in conjunction with calculus of variations, we finds that the necessary boundary conditions are those of classical homogeneous plate theory plus those of an inplane elasticity problem.
