Simply-Supported Elliptical Auxetic Plates

While the maximum bending moment, and hence maximum bending stress, of a fully clamped elliptical plate under uniform load is independent from the Poisson's ratio of the plate material, the same cannot be said so when the plate is simply supported. This paper develops a simple but sufficiently accurate model for evaluating the bending stresses along the principal axes of a simply supported elliptical under uniform load. Plotted results suggest that bending stresses at plate center along the longer principal axis is minimized by the use of highly auxetic materials if the elliptical plate is almost circular but the use of mildly auxetic material is preferred if the aspect ratio of the elliptical plate is very high. Results also reveal that bending stresses at plate center along the shorter principal axis is minimized when the plate material is highly auxetic. Upon considering the von Mises stress state as the effective stress, it was found that the maximum effective stress is reduced with the use of auxetic and conventional materials for simply supported elliptical plates of low and high aspect ratios, respectively.