Stability and initial post-buckling of a standing sandwich beam under terminal force and self-weight

Beams (columns) subjected to axially distributed load (e.g., self-weight) are commonly treated using the classical Euler–Bernoulli beam theory, which ignores the transverse shear effect. Adopting the Engesser and Haringx shear theories, respectively, we study in this article the stability and initial post-buckling of sandwich (or laminated composite) beams under terminal force and axially distributed load. Nonlinear governing equations are derived from geometrical compatibility, equilibrium of forces, and moments. The critical buckling load, modal shapes of deformation, and shear force together with bending moment at buckling can be obtained by using the Galerkin’s method in terms of trigonometric functions, and the initial post-buckled configuration of the beam is determined employing the shooting method. Predictions based on the Engesser theory agree with finite element simulation results, while the Haringx theory overestimates the buckling load. The effects of transverse shear and various different end constraint conditions on static buckling and initial post-buckling of sandwich beams are systematically explored.