Temperature-Dependent Elastic Instability of Porous FG Nanobeams Using a Novel Shape Function and Iterative Computational Procedure based on Nonlocal Eringen Theory

Higher-order theories enhance structural analysis by explicitly accounting for transverse shear effects via a parabolic stress distribution through the beams thickness direction. Various shape functions have been proposed to support this approach. In this study, the temperature‑dependent influence on the stability behavior of nanobeams is examined by introducing a novel shape function into the displacement field and integrating it with the nonlocal Eringen’s theory to derive the governing stability equations. By applying a refined Navier solution method and the iterative computational procedure, we obtain the critical buckling temperatures for two boundary conditions. The accuracy of the model is confirmed through comparison with existing literature, demonstrating excellent agreement. Furthermore, a comprehensive 3D parametric analysis explores the influence of key parameters on the thermal buckling response of nanobeams with temperature-dependent effect.