Refined shear correction factor for very thick simply supported and uniformly loaded isosceles right triangular auxetic plates

Abstract

For moderately thick plates, the use of First order Shear Deformation Theory (FSDT) with a constant shear correction factor of 5/6 is sufficient to take into account the plate deflection arising from transverse shear deformation. For very thick plates, the use of Third order Shear Deformation Theory (TSDT) is preferred as it allows the shear strain distribution to be varied through the plate thickness. Therefore no correction factor is required in TSDT, unlike FSDT. Due to the complexity involved in TSDT, this paper obtains a more accurate shear correction factor for use in FSDT of very thick simply supported and uniformly loaded isosceles right triangular plates based on the TSDT. By matching the maximum deflections for this plate according to FSDT and TSDT, a variable shear correction factor is obtained. Results show that the shear correction factor for the simplified TSDT, i.e. 14/17, is least accurate. The commonly adopted shear correction factor of 5/6 in FSDT is valid only for very thin or highly auxetic plates. This paper provides a variable shear correction for FSDT deflection that matches the plate deflection by TSDT. This variable shear correction factor allows designers to justify the use of a commonly adopted shear correction factor of 5/6 even for very thick plates as long as the Poisson's ratio of the plate material is sufficiently negative.

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.…”

“…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]...…”

“…[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.…”

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

“…Table 3 summarizes the improved shear correction factors of very thick plates evaluated at the plate centroid for three different Poisson's ratio within isotropic solids: extremely auxetic (v = − 1), typical solids (v = 0.3), and incompressible solids (v = 0.5). The plates considered for comparison are simply supported isosceles right triangular plate (Lim, 2016a), equilateral triangular plate (Lim, 2016b), square plate, and rectangular plate of aspect ratio 4 under uniform load and possess the dimensionless plate thickness of h/a = 0.2. a b Fig. 2 Shear correction factor versus Poisson's ratio of a simply supported rectangular plate under uniform load with a variation in relative thickness for a square plate and b variation in aspect ratio for a thick plate The descriptions of shear correction factors developed herein apply only for rectangular plates of simply supported boundary condition, and are therefore not applicable for thick rectangular plates of clamped and/or free edges.…”