Improved shear correction factors for deflection of simply supported very thick rectangular auxetic plates

Abstract

Background: The first-order shear deformation theory (FSDT) for plates requires a shear correction factor due to the assumption of constant shear strain and shear stress across the thickness; hence, the shear correction factor strongly influences the accuracy of the deflection solution; the third-order shear deformation theory (TSDT) does not require a correction factor because it facilitates the change in shear strain across the plate thickness. Methods: This paper obtains an improved shear correction factor for simply supported very thick rectangular plates by matching the deflection of the Mindlin plate (FSDT) with that of the Reddy plate (TSDT). Results: As a consequence, the use of the exact shear correction factor for the Mindlin plate gives solutions that are exactly the same as for the Reddy plate. Conclusions: The customary adoption of 5/6 shear correction factor is a lower bound, and the exact shear correction factor is higher for the following: (a) very thick plates, (b) narrow or long plates, (c) high Poisson's ratio plate material, and (d) highly patterned loads, while the commonly used shear correction factor of 5/6 is still valid for the following: (i) marginally thick plates, (ii) square plates, (iii) negative Poisson's ratio materials, and (d) uniformly distributed loadings.

Shear Deformation in a Class of Thick Hexagonal Plates

“…[50] Following up from analyses on thin auxetic plates [51][52][53] as well as thick auxetic plates based on First-order Shear Deformation Theory (FSDT), [54][55][56] recent effort has shifted to understanding the effect of auxeticity on thick plates using Thirdorder Shear Deformation Theory (TSDT). [57][58][59] Insofar as analysis on auxetic plates is concerned, there is a lack in the literature on thick hexagonal plates; this lack is currently addressed in the present paper. Specifically, this paper benchmarks the Mindlin plate theory (FSDT) against the Reddy plate theory (TSDT) to extract a refined shear correction factor for thick hexagonal plates based on Conway's point matching method for thin hexagonal plates (CPT), and thereafter discusses the effect of material auxeticity on the plate deformation.…”

“…Two‐phase composites or structures have been presented by some authors, as well as for thermoauxetic composites investigated by Strek et al and Jopek et al It is worth also to notice current research on auxetic materials and structures presented in Auxetics 2016 and similar series of conferences, reviews by Saxena et al and Lim, and a monograph . Following up from analyses on thin auxetic plates as well as thick auxetic plates based on First‐order Shear Deformation Theory (FSDT), recent effort has shifted to understanding the effect of auxeticity on thick plates using Third‐order Shear Deformation Theory (TSDT) . Insofar as analysis on auxetic plates is concerned, there is a lack in the literature on thick hexagonal plates; this lack is currently addressed in the present paper.…”

“…Comparison of shear correction factors for the presently investigated hexagonal plate with other polygonal plates[57][58][59] under uniform load with simply supported edges.…”

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

“…[27,28] While the early and subsequent years of auxetic research has been performed on micromechanical modeling to understand the structure-property-processing relationships that give rise to auxetic behavior in bulk solids, there has been an increasing trend toward effort to comprehend the effect of auxeticity on membranes, [29][30][31] rods, [32][33][34] beams, [35][36][37] shells, [38][39][40] and 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]...…”

Simplified Design Equations for a Class of Rhombic Auxetic Plates

“…Investigations into the performance of plates with the use of auxetic materials have been carried out [8][9][10][11]. Although studies on auxetic plates have been done on rectangular [12][13][14], circular [15][16][17], triangular [18][19][20], elliptical [21], sectorial [22], hexagonal [23] and regular polygonal [24] plates-no work has been done on auxetic rhombic plates. 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 simply supported and uniformly loaded, with special emphasis on the use of auxetic materials.…”