Hygrothermal effects on buckling behaviors of porous bi-directional functionally graded micro-/nanobeams using two-phase local/nonlocal strain gradient theory

Rapid development of technology puts forward higher performance requirements for advanced materials with multi-field coupling stability. The porous functionally graded materials, which is well developed with mature design, tools, can be customized according to specific application through nanostructures. In this work, the influences of hygro-thermo-mechanical coupling loadings on buckling behaviors of porous bi-directional functionally graded (2D FG) Timoshenko nanobeam is investigated through the numerical study. The governing equation and boundary conditions are derived on the basis of two phase local/nonlocal strain gradient theory employing the principle of virtual work, and a processing method for Clamped-Free (C–F) boundary condition is proposed. By employing generalized differential quadrature method (GDQM), the theoretical solution of buckling behavior of the Timoshenko nanobeam is obtained, with the implementation of comparison and convergence studies to demonstrate the accuracy and effectiveness. On the best of the authors’ knowledge, it is novel to investigate the buckling response of 2D FG Timoshenko nanobeam under hygrothermal environment using the two local/nonlocal strain gradient theory. Herein, the influence of nonlocal parameter, strain gradient theory, aspect ratio, axial gradient index, thickness gradient index, hygrothermal loadings and local volume fraction on the critical buckling load under various natural boundary conditions are acquired and discussed. The numerical results indicate that the present model can capture the buckling response of porous 2D FG Timoshenko nanobeams under hygrothermal environment, exhibiting consistent softening/hardening effects under all boundary conditions and modes. [Display omitted] •An comprehensive analytical model of porous 2D FG Timoshenko micro/nanobeamconsidering the small size effect is proposed.•The hygrothermal effect on buckling stability of 2D FG micro/nanobeam is studied.•An efficient and accurate GDQM for hygrothermal buckling stability is proposed.