A size-dependent functionally graded nanocomposite Mindlin plate model based on consistent generalized continuum theory. (English) Zbl 1543.74062
Summary: This paper presents an effective consistent-continuum model to analyse the behaviour of functionally graded nanocomposite (FG-NC) Mindlin plates based on the consistent couple stress theory (CCST) and the non-classical finite element method. A novel unified form is presented based on the Halpin-Tsai model to capture the small-scale heterogeneity, which can simultaneously consider the grading effects of the matrix and reinforcement phases along with the dispersion distribution through the plate thickness. To meet the \(\mathrm{C}^1\) continuity requirements of the couple stress theory, a four-node rectangular element is adopted by using the Hermitian approach and in the way of a sub-parametric manner. The element has 20 degrees of freedom (DOF) at each node, which is reduced to 12 DOF in a bending mode without stretching deformation. FG-NC plates’ bending, free vibration, and buckling behaviour are investigated. Graphene oxide (GO), reduced graphene oxide (rGO), and silver-reduced graphene oxide (Ag-rGO) are considered for the dispersed phase. Size-dependent optimal values for the material and geometrical properties of the FG-NC plate model are presented, which minimize its mass with the frequency constraint. The effects of various parameters such as grading index, weight fraction, dispersion pattern, filler aspect/thickness ratio, and length scale parameter are examined, and benchmark examples are provided.
MSC:
| 74K20 | Plates |
| 74E30 | Composite and mixture properties |
| 74M25 | Micromechanics of solids |
| 74E05 | Inhomogeneity in solid mechanics |
Keywords:
Halpin-Tsai model; graphene-based reinforcement; consistent couple stress theory; non-classical finite element methodReferences:
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