Static and free vibration analysis of functionally graded carbon nanotube reinforced skew plates

Abstract

Highlights • Invariant definition of the transversely isotropic constitutive tensor based on representation theorem of functionally graded materials (FGM) in oblique coordinates. • Study of influence of fiber direction and skew angle on natural frequencies of (FGM) nanocomposite skew plates. • Consideration of one asymmetric and three symmetric distributions of functionally graded nanocomposite skew plates. • The underlying shell theory is formulated in oblique coordinates, based on the Hu-Washizu principle and first-order shear deformation theory (FSDT). • Independent approximations of displacements, strains and stresses.

Metamodel-based approach for stochastic free vibration analysis of functionally graded carbon nanotube reinforced plates

“…1. In this section, the more general theoretical formulation developed in [16] is adopted here for the case of flat rectangular shells. Denoting by U(γ) the strain energy and by γ and σ the vectors containing the strain and stress components, respectively, a modified potential of Hu-Washizu assumes the form […”

“…They concluded that the geometric parameters such as side angle, thickness-to-width ratio or plate aspect ratios are more significant than material parameters such as CNT distribution and CNT volume fraction. García-Macías et al [16] proposed a shell finite element formulation based on the Hu-Washizu principle in general curvilinear coordinates for the simulation of FG-CNTRCs. In particular, it is applied for an exhaustive parametric analysis of the static response and free vibration characteristics of FG-CNTRC skew plates with uniform and linear CNT distributions.…”

“…Furthermore, the efficacy of both metamodels are compared to direct Monte Carlo simulation (MCS) with accurate results and a drastic reduction of computation cost. Motivated by [16], a finite element formulation based on a modified Hu-Washizu potential principle is employed. Four-noded elements with five degrees of freedom at each node are implemented with consideration of transverse shear strains by first-order shear deformation theory (FSDT).…”

Vibration analysis of CNT-reinforced functionally graded composite cylindrical shells in thermal environments

“…The first-order shear deformation theory (FSDT) was applied to the structural modeling. García-Macías et al [17] provided numerical results for static and dynamic simulations of CNT-reinforced skew plates. Zhang et al [18] and Lei et al [19][20][21] investigated the static, dynamic and buckling properties of FG-CNT reinforced composite plates, laminated plates androtating cylindrical panels using the element-free kp-Ritz method.…”

Vibration of functionally graded carbon nanotube reinforced quadrilateral plates using geometric transformation discrete singular convolution method

“…Garcia‐Madias et al elaborated an efficient finite element method in conjunctions with Hu‐Washizu principle for static and dynamic analysis of skew plates for CNT reinforced composite material. By using the differential quadrature method, free vibration analysis of quadrilateral laminated plates with CNT reinforced composite is studied by Malekzadeh and Zarei .…”