Nonlinear stability of curved multi-phase composite panels: influence of agglomeration in randomly distributed carbon nanotubes with non-uniform in-plane loads

The nonlinear stability characteristics of doubly curved panels made of three-phase composites with randomly dispersed carbon nanotubes (RD-CNTRFC) subjected to practically-relevant non-uniform in-plane loads are investigated in this study. Carbon nanotubes, when mixed with resin polymer, may give rise to bundles, termed as agglomerations, which can have a profound impact on the effective material properties. There exists a strong rationale to investigate the influence of such agglomeration on the nonlinear equilibrium path of panels, which can subsequently be included in the structural stability design process to enhance operational safety. A multi-stage bottom-up numerical framework is developed here to probe the nonlinear stability characteristics. The effective material properties of RD-CNTRFC panels are determined using the Eshelby-Mori-Tanaka approach and the Chamis method of homogenization. By considering von-Kármán non-linearity and Reddy's higher-order shear deformation theory, strain-displacement relations are established for the non-linear stability analysis. The governing partial differential equations are simplified into nonlinear algebraic relations using Galerkin's method. Subsequently, by reducing the stiffness matrix neglecting the non-linear terms and solving the Eigenvalue problem, we obtain critical load and non-linear stability path of shell panels based on arc-length approach. In the present study, various shell geometries such as cylindrical, elliptical, spherical and hyperbolic shapes are modeled along with the flat plate-like geometry to investigate the non-linear equilibrium paths, wherein a geometry-dependent programmable softening and hardening behavior emerges