Shear Deformation in a Class of Thick Hexagonal Plates

Abstract

The shear deformation characteristics of a simply supported and uniformly loaded regular hexagonal plate is investigated herein, including cases when the plate is made from auxetic materials. Specifically, the shear correction factor for such a plate is obtained by matching its maximum deflections between the Mindlin and Reddy plate theories after a convenient Kirchhoff theory model has been proposed. Results show that the shear deformation is suppressed if the plate material is auxetic; for example, the extent of shear deformation is conserved even if the plate thickness is doubled, provided that the Poisson's ratio reduces from 0.5 to −1. When benchmarked against other plate shapes, the shear deformation for the hexagonal plate is comparable with those of square and equilateral triangular plates. Therefore, the design principles that incorporate shear deformation in thick square plates and in thick equilateral triangular plates can be extended to thick hexagonal plates, and this validity applies for both conventional and auxetic plate materials.

Auxetics and Other Systems of Anomalous Characteristics

“…The paper shows that the interplay between boundary conditions and auxeticity is important to defi ne the global deformation mechanism of those plates: stiffening effects for negative Poisson's ratio materials do arise for SSF conditions, and quite interestingly the opposite when all the three edges are simply supported. [21] concerns the shear correction factor for a simply supported and uniformly loaded regular hexagonal plate. Results of the investigations show that the shear deformation is suppressed if the plate material is auxetic.…”

Auxeticity of Concentric Auxetic-Conventional Foam Rods with High Modulus Interface Adhesive

“…It has also been found that novel properties, distinct from conventional or auxetic materials, arise when a composite structure is made from both conventional and auxetic materials. In addition to a recent comprehensive survey of auxetic materials and structures [ 37 ], the reader is also referred to a recent focus issue on “auxetics and other systems of anomalous characteristics” [ 38 , 39 , 40 , 41 , 42 ], as well as papers in this special issue [ 43 , 44 , 45 , 46 , 47 , 48 ].…”

An Accurate Design Equation for the Maximum Deflection in a Class of Auxetic Sectorial Plates

“…[41][42][43][44] In the case of plates, the effect of material auxeticity has been investigated on problems of the following mechanical nature: a) static, [45][46][47][48] b) dynamic, [49][50][51][52][53][54] c) thermoelasticity and/or thermal stresses, [55][56][57][58][59] d) instability, [59][60][61][62] e) first-order and higher-order shear deformation, [62][63][64][65][66][67] as well as f) plates of unconventional shapes. [66][67][68][69][70][71] To date no investigation has been made on the performance of auxetic materials in the form of sectorial plates. Sectorial plates have traditionally been used for engineering applications such as double acting fluid motors [72] and rotary port for the aircraft, [73] and are continued to be investigated and/or applied in aerospace, nuclear and other engineering applications.…”