On the thermally induced non-linear response of functionally graded beams

Abstract

The current paper presents an analytical investigation on the thermally induced non-linear response of shear-deformable slightly curved beams made of functionally graded materials. It is supposed that the temperature-dependent material properties of beam vary continuously along its thickness according to a power law. First-order shear deformation theory of beam in conjunction with neutral surface concept is implemented to establish the geometrically non-linear equilibrium equations of system under in-plane thermal loading. Subsequently, an analytical solution is presented to trace the equilibrium path of system with fully clamped boundary conditions. It is indicated that the system may undergo a perturbed pitchfork bifurcation at a critical temperature rise. Furthermore, it is shown that the initial configuration of system can't be considered as its equilibrium path before the onset of bifurcation. A comprehensive investigation is conducted to highlight the role of different parameters i.e., the length-to-thickness ratio, the amplitude of initial curvature, the power-law exponent, and the type of thermal loading in the non-linear response of system. Eventually, the influence of geometric nonlinearity on the thermally induced response of system is studied by comparing the results of linear and non-linear models.