An Analytical Study on the Thermal Post-Buckling Behaviors of Geometrically Imperfect FRC-Laminated Beams Using a Modified Zig-Zag Beam Model

An asymptotic analytical method is proposed to study the thermal post-buckling behaviors of fiber-reinforced composite (FRC)-laminated beams with geometric imperfections employing a modified zig-zag beam model. The beam model satisfied the discontinuity of the shear deformation at the interlayer interfaces and the stress boundary conditions on the upper and lower surfaces. Each imperfection was assumed to possess the same shape as the buckling mode, and the in-plane boundary conditions were presumed to be immovable. A two-step perturbation method was used to solve the nonlinear governing equations and obtain the equilibrium path. Subsequently, the initial defect sensitivity of the post-buckling behaviors was analyzed. The existence of the bifurcation-type equilibrium path for perfect beams is discussed in depth. Load–deflection curves for beams with various boundary conditions and ply modes were plotted to illustrate these findings. The effects of the slenderness ratio, elastic modulus ratio, thermal expansion coefficient ratio, ply modes, and supported boundaries on the buckling and post-buckling behaviors were also investigated. The numerical results indicate that the slenderness ratio significantly influences the critical buckling temperature, with thicker beams exhibiting higher buckling resistance. The elastic modulus ratio also plays a crucial role, with higher ratios leading to increased buckling strength. Additionally, the thermal expansion coefficient ratio affects the post-buckling load-bearing capacity, with lower ratios resulting in greater stability.