Shear Correction Factors for Functionally Graded Plates

Abstract

The Reissner-Mindlin plate model for calculation of functionally graded materials has been proposed in literature by using shear correction coefficient of homogeneous model. However, this use is a priori not appropriate for the gradient material. Identification of the transverse shear factors is thus investigated in this paper. The transverse shear stresses are derived by using energy considerations from the expression of membrane stresses. Using the obtained transverse shear factor, a numerical analysis is performed on a simply supported FG square plate whose elastic properties are isotropic at each point and vary through the thickness according to a power law distribution. The numerical results of a static analysis are compared with available solutions from previous studies.

Transverse shear stiffness of a chevron folded core used in sandwich construction

“…Yet, in practical applications, the contrast assumption is not always fulfilled which limits the validity of this method. Another proposal, made by Cecchi and Sab (2007) (as well as, Cecchi and Sab (2004), Nguyen et al (2005b), Cecchi and Sab (2007), Nguyen et al (2007Nguyen et al ( , 2008), is based on Whitney (1972) work on the derivation of shear correction factors for laminates. This seminal work is extended to heterogeneous plates thanks to an energetic equivalence.…”

A study on the structural behaviour of FGM plates static and free vibrations analyses

“…In Table 2, one can observe the non-dimensional maximum deflections obtained using the implemented methods and the results of Nguyen et al [6]. The multiplier used for this purpose is…”

“…One starts by considering in sub-section 4.1 two examples related to the static and free vibrations analyses of functionally graded plates, which goal is to validate the present implemented models, regarding a reference work [6]. All studies are based on the FSDT.…”

“…[ For the sake of the table simplicity and interpretation clearness, it should be noted that for each aspect ratio value the values are multiplied by the value that is next to the reference results row, in the "Method" column, namely [6]x10 -6 , [6]x10 -5 , [6]x10 -4 .…”

“…[ Three different aspect ratios (a/h) between the plate edge (a) and the thickness (h) were considered, namely: 5, 10 and 20, as well as three distinct shear correction factors k: 1 (without shear correction), 5/6 and 0.576 [6].…”