Optimal Poisson’s ratios for laterally loaded rectangular plates

Abstract

Although most materials used in practice possess positive Poisson’s ratio in the range 0 to ½, there has been increasing number of auxetic materials being developed and investigated. The counter-intuitive property of auxetic materials opens up the possibility of solids and structures that behave in ways that have been overlooked in the past but are nevertheless consistent with physical laws. This article investigates how the auxeticity of a plate material influences the stresses and moments arising from lateral loads. Using classical plate theories, the optimal Poisson’s ratio of simply supported rectangular plates under lateral loads are obtained on the basis of (a) stress minimization from the maximum bending and shearing stresses, and (b) moment minimization from the maximum bending and twisting moments. Results from stress minimization shows that the optimal Poisson’s ratio is strongly influenced by the relative plate thickness and plate aspect ratio. Using the example of a simply supported rectangular plate under sinusoidal load, the optimal Poisson’s ratio becomes more negative for higher aspect ratio. In addition, the optimal Poisson’s ratio becomes more negative, until a limit of −1 is reached, for decreasing relative plate thickness. Results from moment minimization reveal that the optimal Poisson’s ratio is strongly influenced by the load distribution. For a square plate, the optimal Poisson’s ratio is a negative value if the load distribution is more concentrated than a sinusoidal load or if the central square patch of uniform load takes up less than 43% of the plate area. These results suggest the usefulness of auxetic materials for lowering the stresses and moments in rectangular plates under most loading conditions.