Abstract
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. 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). 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. 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.
Highlights
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; 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
In determining the range of relative thickness that is applicable for the shear deformation theories, one may refer to Steele and Balch (2009) who classified the plate thickness into four categories: (i) a/h > 100, (ii) 20 < a/h < 100, (iii) 3 < a/h < 20, and (iv) a/h < 3
This implies that one may adopt the membrane theory for h/a < 0.01, classical plate theory (CPT) for h/a < 0.05, shear deformation theories for h/a < 0.3333, and elasticity theory for h/a > 0.3333. It follows that the TSDT-based shear correction factor for FSDT problems are applicable for relative thickness range of h/a < 0.3333
Summary
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; 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. Exact shear correction factors for supported very thick rectangular Mindlin plates are derived by comparing its deflection against that of Reddy plates.
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