Simplified Design Equations for a Class of Rhombic Auxetic Plates

Teik-Cheng Lim,C.W Lim,Xiaohong Zhu

doi:10.1051/matecconf/201820601009

Teik-Cheng Lim, C.W Lim + Show 1 more

Open Access

https://doi.org/10.1051/matecconf/201820601009

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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.

Highlights

The Poisson’s ratio of materials is normally assumed to be positive, with a value of v = 0.3 being typically assigned for isotropic materials
The Poisson’s ratio of anisotropic solids has no bounds [1], it has been shown that the Poisson’s ratio in the case of isotropic materials are bounded within -1 v 0.5 [2]; solids with negative Poisson’s ratio have been studied [3]
A number of auxetic materials applications have been suggested; interested readers are referred to related reviews [4,5,6] and a monograph [7] for further details of such materials

Summary

Introduction

The Poisson’s ratio of materials is normally assumed to be positive, with a value of v = 0.3 being typically assigned for isotropic materials. The Poisson’s ratio of anisotropic solids has no bounds [1], it has been shown that the Poisson’s ratio in the case of isotropic materials are bounded within -1 v 0.5 [2]; solids with negative Poisson’s ratio have been studied [3]. Investigations into the performance of plates with the use of auxetic materials have been carried out [8,9,10,11]. This paper aims to provide a set of design equations that is simple to execute and sufficiently accurate for a class of rhombic plates, which are supported and uniformly loaded, with special emphasis on the use of auxetic materials

Preamble to thin rhombic plates

Semi-empirical modelling for thin rhombic plates

First-order shear model for thick rhombic plates

Conclusions and recommendations

A11 A12 A1M b1 A1