On boundary conditions for thermally loaded FG beams

As a functionally graded extensible beam is subjected to the in-plan thermal loading, distinct scenarios occur depending on the boundary conditions of system. Analyzing the thermo-mechanical behavior of system by employing the simplified boundary conditions (neglecting the influence of thermal moment at the original boundary conditions of system) leads to prediction of inaccurate trends and results. Although, the problem based on the original boundary conditions was solved by some researchers, there exist remarkable amount of linear and nonlinear studies from macro to small scale based on the classical and non-classical theories by implementation of the simplified boundary conditions. In the present work, the thermo-mechanical equilibrium paths and free flexural vibration of system based on the simplified and original boundary conditions are compared to show the inaccuracy of simplified boundary conditions-based analysis. In this study, two distinct types of thermal loading i.e., uniform temperature rise and heat conduction across the thickness are considered. In addition, it is indicated that the original boundary conditions-based linear analysis for evaluation of the equilibrium path of system yields inaccurate trend.