A closed form dynamic stiffness formulation for buckling analysis of FG-CNTRC plate and plate assemblies with internal line support

Abstract

The primary aim of this study is to analyze the buckling behavior of carbon-nanotubes (CNT) reinforced plates using a closed-form dynamic stiffness formulation. The dynamic stiffness method (DSM), typically employed for analyzing plate vibrations, is adapted here for the buckling analysis of various configurations of CNT-reinforced composite plates with internal line support and subjected to uniaxial and biaxial in-plane loads. The displacement field is based on the first-order shear deformation theory, and the analytical expressions for governing differential equations and natural boundary conditions are derived via Hamilton’s principle. The dynamic stiffness matrix is developed for individual plate elements, considering Levy-type boundary conditions. These matrices are then combined to form a global dynamic stiffness matrix, which is solved using the Wittrick–Williams (W–W) algorithm to obtain the critical buckling load. A comprehensive comparative analysis is undertaken to ascertain the accuracy and computational efficacy of the present DSM with alternative numerical methodologies, alongside detailed parametric studies to explore plate buckling characteristics. It should be noted that the DSM is known to provide accurate results as it is based on the exact governing differential equation. Therefore, the reported buckling results can serve as a benchmark for future research in this field.