Analytical determination of non-local parameter value to investigate the axial buckling of nanoshells affected by the passing nanofluids and their velocities considering various modified cylindrical shell theories

We analytically determine the nonlocal parameter value to achieve a more accurate axial-buckling response of carbon nanoshells conveying nanofluids. To this end, the four plates/shells’ classical theories of Love, Flügge, Donnell, and Sanders are generalized using Eringen’s nonlocal elasticity theory. By combining these theories in cylindrical coordinates, a modified motion equation is presented to investigate the buckling behavior of the nanofluid-nanostructure-interaction problem. Herein, in addition to the small-scale effect of the structure and the passing fluid on the critical buckling strain, we discuss the effects of nanoflow velocity, fluid density (nano-liquid/nano-gas), half-wave numbers, aspect ratio, and nanoshell flexural rigidity. The analytical approach is used to discretize and solve the obtained relations to study the mentioned cases.