Dynamic analysis of stiffened functionally graded composite plates reinforced by carbon nanotubes subjected to blast loads using a new four-variable refined plate theory

Abstract

In this paper, a new four-variable refined plate theory for dynamic analysis of stiffened functionally graded composite plates reinforced by carbon nanotubes (SFG-CNTRC) subjected to blast loadings is developed. The governing equations of the system are obtained using the finite element method. The Newmark’s time integration is used to solve the vibration equations for determining the dynamic response of the plates. To check the validity of the present formulation, numerical results are compared with the previous data in the literature. The effects of volume fraction of carbon nanotubes, thickness of the plate, and boundary conditions of the plate on the dynamic response of the SFG-CNTRC are studied.

Static stability study of stiffened functionally graded composite plates reinforced by carbon nanotubes using finite element method

“…In their study, Daouadji TH and Tounsi A [14] used a new higher-order shear deformation theory on static analysis of FG plates. N. T. Chung et al [15] analyzed the dynamic of the stiffened functionally graded composite plates reinforced by carbon nanotubes (SFG-CNTRC) under a blast load system using FEM and a new polynomial shear deformation function.…”

“…The structure of a SFG-CNTRC and load subjected to the plate In all distributions, the law of uniform distribution (UD) is the uniform distribution of CNTs in the cross-section of the plate, while the law of asymmetrical distribution (FG-V) or symmetrical distributions (FG-O, FG-X) is the dependence of the density of CNTs on the plate thickness variable. Accordingly, the mathematical model of the distribution of CNTs along the thickness direction of the plate is as follows [15], [16], [17], [21], [23]: In all distributions, the law of uniform distribution (UD) is the uniform distribution of CNTs in the cross-section of the plate, while the law of asymmetrical distribution (FG-V) or symmetrical distributions (FG-O, FG-X) is the dependence of the density of CNTs on the plate thickness variable. Accordingly, the mathematical model of the distribution of CNTs along the thickness direction of the plate is as follows [15][16][17][18][19]:…”

“…Accordingly, the mathematical model of the distribution of CNTs along the thickness direction of the plate is as follows [15], [16], [17], [21], [23]: In all distributions, the law of uniform distribution (UD) is the uniform distribution of CNTs in the cross-section of the plate, while the law of asymmetrical distribution (FG-V) or symmetrical distributions (FG-O, FG-X) is the dependence of the density of CNTs on the plate thickness variable. Accordingly, the mathematical model of the distribution of CNTs along the thickness direction of the plate is as follows [15][16][17][18][19]:…”

“…with w CNT is the mass fraction of the CNTs, and ρ CNT and ρm are the densities of the CNTs and the matrix, respectively. The effective properties of the FG-CNTRC lamina can be determined as follows [10,15,19]:…”

“…in which u 0 , v 0 , and w 0 are the displacements of the corresponding point on the midplane, respectively; w b and w s denote the bending and shear components of the transverse displacement, respectively; f (z) is the correction function of the transverse shear strains. In this study, the correction function of shear strain is determined as follows [15]: The nonlinear von Karman strain-displacement equations are as follows [19]:…”