# Numerical Investigation of Buckling Behavior of MWCNT-Reinforced Composite Plates

## TL;DR

This paper investigates how adding MWCNTs to composite plates affects their buckling behavior using a new mathematical model and simulation.

## Contribution

A novel higher-order shear and normal deformation theory is introduced for analyzing MWCNT-reinforced composite plates.

## Key findings

- The hybrid HSNDT model accurately predicts buckling behavior without requiring a shear correction factor.
- The model with seven degrees of freedom reduces computation time for parametric studies.
- Results were validated through convergence studies and comparison with existing literature.

## Abstract

The current study demonstrates the buckling properties of composite laminates reinforced with MWCNT fillers using a novel higher-order shear and normal deformation theory (HSNDT), which considers the effect of thickness in its mathematical formulation. The hybrid HSNDT combines polynomial and hyperbolic functions that ensure the parabolic shear stress profile and zero shear stress boundary condition at the upper and lower surface of the plate, hence removing the need for a shear correction factor. The plate is made up of carbon fiber bounded together with polymer resin matrix reinforced with MWCNT fibers. The mechanical properties are homogenized by a Halpin–Tsai scheme. The MATLAB R2019a code was developed in-house for a finite element model using C0 continuity nine-node Lagrangian isoparametric shape functions. The geometric nonlinear and linear stiffness matrices are derived using the principle of virtual work. The solution of the eigenvalue problem enables estimation of the critical buckling loads. A convergence study was carried out and model efficiency was corroborated with the existing literature. The model contains only seven degrees of freedom, which significantly reduces computation time, facilitating the comprehensive parametric studies for the buckling stability of the plate.