Post-buckling behavior of porous magneto-electro-elastic nano-cylindrical shells based on nonlocal strain gradient theory

Porous magneto-electro-elastic (PMEE) nanoshells offer lightweight, field-tunable structural concepts for nano-electromechanical systems, but their post-buckling response is governed simultaneously by porosity, small-scale mechanics, geometric nonlinearity, and multi-field coupling. This study develops a nonlinear model based on the nonlocal strain gradient theory (NSGT) for functionally graded PMEE cylindrical nanoshells using Kirchhoff-Love kinematics, von Kármán nonlinearity, coupled magneto-electro-elastic constitutive relations, and Galerkin continuation. Symmetric/asymmetric cosine porosity distributions and distinct symmetric/asymmetric buckling branches are considered. Modal convergence and two quantitative benchmark families in the local homogeneous elastic limit support the numerical implementation; the maximum discrepancies from published critical-load data are 0.00752% and 0.02450%. At w max /h = 0.38, increasing the porosity coefficient from 0 to 0.4 reduces the normalized load by 19.3–22.4%. Increasing e 0 a/h from 0 to 0.4 lowers the load by 0.83–2.16%, whereas increasing l m /h over the same range raises it by 1.63–2.22%, clearly separating nonlocal softening from strain-gradient hardening. Electric and magnetic potentials provide systematic but sub-1% tuning over the studied ranges. Increasing L/h reduces the critical load by 0.51–6.34% and can induce post-buckling branch crossings. The results identify porosity as the dominant load-level parameter, with size effects, fields, and geometry providing mode-dependent secondary control.