Stochastic analysis of FG-CNTRC conical shell panels based on a perturbation stochastic meshless method without partial derivative

Abstract

This study introduces the spatial variability of material parameters into the free vibration analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) conical shell panels, using the modified perturbation stochastic method (MPSM) to handle low uncertainty. Based on the first-order shear deformation shell theory, the approximate displacement field is represented by the shape function of the kernel particle. The Young's moduli of carbon nanotubes (CNTs) and the matrix are regarded as one-dimensional (1D) and two-dimensional (2D) random fields, respectively, which are discretized by the Karhunen-Loève (K-L) expansion. The random fields in the rectangular area are extended to the conical area, establishing the random fields for the conical shell panel, and plotting the first six eigenvalue drop point line graphs and eigenfunction diagrams for the conical shell panel. The obtained random variables are substituted into the modified perturbation stochastic method and the Reproducing Kernel Particle Method (RKPM) to calculate the first two-order estimates of the stochastic dimensionless natural frequencies $\bar{\omega }$. The sensitivity of the first to fourth $\bar{\omega }$ to the random fields, the impact of multiple random variables, and multiple random fields on $\bar{\omega }$ are analyzed, and the corresponding stochastic bands are plotted. The results indicate that $\bar{\omega }$ is mainly influenced by the random fields $E_{11}^{\text{CNT}}$​ and $E_{22}^{\text{CNT}}$, and the distribution pattern of carbon nanotubes affects the sensitivity.