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This contribution presents a new methodology and a new indeterminate integral variable of displacement field using trigonometric deformation in conjunction with gradient elasticity theory. The aim, for the first time, is to explore the thermal buckling behavior of functionally graded (FG) nanobeam thus elastic gradient theory takes into account the size effect on the critical thermal buckling load of FG nanobeams. Secondly, the impact of various factors, such as nonlocal coefficient, porosity parameter, material index, thermal loading type, and aspect ratio on the critical thermal buckling load of FG nanobeams. The material characteristics are considered to vary in thickness as the power law varies and the pore network is assumed to be empty or filled with low-pressure air.
Ellali et al. (Mon,) studied this question.