An Analytical Study on 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 satisfies the discontinuity of the shear deformation at the interlayer interfaces and the stress boundary conditions on upper and lower surfaces. The imperfection is assumed to possess the same shape as the buckling mode and the in-plane boundary conditions supposed immovable. A two-step perturbation method is used to solve the nonlinear governing equations and obtain the equilibrium path. Subsequently, the initial defect sensitivity of the post-buckling behaviors is analyzed and the existence of the equilibrium path of bifurcation type of perfect beams is discussed in depth by plotting the load-deflection curves of beams with different boundary conditions and ply modes. Effects of slenderness ratio, elastic modulus ratio, thermal expansion coefficient ratio, ply modes, supported boundaries on the buckling and post-buckling behaviors are also investigated. Numerical results suggest the necessity to consider the zig-zag displacement fields for buckling instability analysis of general asymmetric FRC laminated beams when the thickness of the beams or the ratio of the two in-plane Young’s moduli is large.