# Buckling Analysis of CNTRC Curved Sandwich Nanobeams in Thermal Environment
An efficient alternative tool to handle nonlocalities within nanostructures is represented by the strain gradient theory, as successfully applied in [19; 20] for the thermal snap-buckling and bending analysis of FG curved porous and non-porous nanobeams and in [21; 22] for the buckling study of porous FG sandwich nanoplates resting on a Kerr foundation due to a heat conduction. A theoretical formulation based on a Reddy shear deformation theory, has been also proposed in the recent work by [PERSON] et al. [23] to study the buckling and vibration of FG-CNTRC-laminated nanoplates in thermal environment, with promising results for engineering applications. Furthermore, [PERSON] et al. [24] investigated the thermal buckling response of FG sandwich beams under a power-law (P-FGM) or sigmoid (SFGM) variation. Further attempts of combining higher order theories and nonlocal approaches in a unified context, can be found in [25; 26; 27; 28] to predict the influence of an axial in-plane load function on the critical buckling load and mode shape of composite beam members, also in presence of porosities. During fabrication, structural members can exhibit an initial curved shape as possible imperfection related to iterative heating and cooling processes. Many MEMS devices employ curved structures as well [29]. The initial curvature of a beam structure can be a source of difficulty in developing the constitutive relations, as verified by [PERSON] et al. [30], who illustrated the possible effects of curvatures and imperfections on the post-buckling and free vibration response of multilayer nonlocal prestressed nanobeams. [PERSON] et al. [31] also studied the effect of nanotube waviness and agglomeration on the elastic property of CNT-reinforced composites. A further systematic study was performed by [PERSON] et al. [32], who investigated the impact of the surface energy and thermal loading on the static stability of curved nanowires, modeled as curved Euler-Bernoulli beams, accounting for both the von Karman and axial strain field. Among more sophisticated shell models, a valuable comparison between different higher-order formulations was proposed in [33; 34; 35] for the static analysis of multilayered composite and sandwich plates and shells, both from a theoretical and computational perspective. [PERSON] et al. [36] later proposed a differential quadrature method to study the nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations. A further attempt of combining the nonlocal strain gradient and higher-order shell theories was conducted by [PERSON] et al. [37] for a wave dispersion study in anisotropic doubly-curved nanoshells, as well as in [38; 39; 40; 41] for FG-CNTRC curved nanobeams also in coupled piezoelectric conditions. In another work, [PERSON] et al. [42] predicted the static deflection and stress field of curved FG-CNTRC nonlocal Timoshenko nanobeams resting on an elastic foundation under four different distribution patterns of CNTs throughout the thickness direction. [PERSON] et al. [43] also presented the influence of periodic and/or nonperiodic imperfections on the buckling, post-buckling and dynamic response of curved beams resting on nonlinear elastic foundations by means of high-performing numerical differential-integral quadrature methods (DIQMs). [PERSON] et al. [44] developed a theoretical model to study the dynamics of non-cylindrical curved viscoelastic SWCNTs by applying a second gradient theory of stress-strain, whereas [PERSON] et al. [45] used an energy equivalent model to study the post-buckling response of imperfect CNTs resting on a nonlinear elastic foundation, including mid-plane stretching and nanoscale effects. Among the most recent works on the topic, [PERSON] et al. [46] developed a novel four-variable refined shell theory to study the free vibration of multilayered FG-CNTRC doubly curved shallow shell panels; [PERSON] et al.