Simplified Design Equations for a Class of Rhombic Auxetic Plates

Abstract

Equations for solving the deflection and bending moments of rhombic plates by exact method are known to be highly tedious. A set of simplified equations is developed for design purposes of such simply supported plates under uniform load. Curve-fitting from exact data allows the deflection and its second derivatives, evaluated at the plate centre, to be expressed in greatly simplified and yet sufficiently accurate empirical models for thin rhombic plates. Using the simplified model, it is shown that the maximum bending moment can be reduced by using auxetic materials. By including the effects of shear deformation for thick rhombic plates, it is demonstrated that the ratio of shear-to-bending deformation decreases as the rhombic plate approaches a square shape and as the plate’s Poisson’s ratio becomes more negative.