Buckling and post-buckling of a compressible slab under combined axial compression and lateral load

Abstract

In this paper, we study the buckling and post-buckling of a compressible hyperelastic slab under both axial compressive force and distributed force on two lateral surfaces. The combined series-asymptotic expansions method is used to obtain the simplified model equations. We further assume that the lateral load is uniformly distributed and is a constant. We discuss three cases: (I) axial compression dominant, (II) lateral compression dominant and (III) uniform compression. In case (I), the lateral stress is given as a constant and no buckling bifurcation will occur when the axial stress is not imposed. In this case, the lateral stress may be compressive or tensile stress. In case (II), the axial compressive stress is given as a constant and no buckling bifurcation will occur when the lateral compressive stress is not imposed. In case (III), the slab is uniformly compressed at two lateral boundaries and two ends of the slab. For all three cases, with sliding-sliding end conditions at two ends, we obtain the approximate expressions of the critical stress values and mode numbers from linear bifurcation analysis and obtain the approximate analytical post-buckling solutions by using the method of multiple scales. We find both supercritical and subcritical bifurcations may occur depending on the material constants, slenderness ratio of the slab and bifurcation modes. The analytical post-buckling solutions are compared with the numerical solutions of the model equations and good agreements are found.