column buckling, plates under buckling loads can continue to carry loads, called local buckling. This phenomenon is incredibly useful in numerous systems, as it allows systems to be engineered to provide greater loading capacities. For a rectangular plate, supported along every edge, loaded with a uniform compressive force per unit length, the derived governing equation can be stated by: where , out-of-plane deflection , uniformly distributed compressive load , Poisson's ratio , modulus of elasticity , thickness The solution to the deflection can be expanded into two harmonic functions shown: where , number of half sine curvatures that occur lengthwise , number of half sine curvatures that occur widthwise , length of specimen , width of specimen The previous equation can be substituted into the earlier differential equation where equals 1. can be separated providing the equation for the critical compressive loading of a plate: where , buckling coefficient, given by: The buckling coefficient is influenced by the aspect of the specimen, / , and the number of lengthwise curvatures. For an increasing number of such curvatures, the aspect ratio produces a varying buckling coefficient; but each relation provides a minimum value for each . This minimum value can then be used as a constant, independent from both the aspect ratio and . Given stress is found by the load per unit area, the following expression is found for the critical stress: From the derived equations, it can be seen the close similarities between the critical stress for a column and for a plate. As the width shrinks, the plate acts more like a column as it increases the resistance to buckling along the plate's width. The increase of allows for an increase of the number of sine waves produced by buckling along the length, but also increases the resistance from the buckling along the width. This creates the preference of the plate to buckle in such a way to equal the number of curvatures both along the width and length. Due to boundary conditions, when a plate is loaded with a critical stress and buckles, the edges perpendicular to the load cannot deform out-of-plane and will therefore continue to carry the stresses. This creates a non-uniform compressive loading along the ends, where the stresses are imposed on half of the effective width on either side of the specimen, given by the following: where , effective width , yielding stress