Nonlinear in-plane buckling of shallow laminated arches incorporating shear deformation under a uniform radial loading

Abstract

This paper is concerned with the nonlinear in-plane buckling of shear deformable laminated composite shallow arches under a uniform radial loading. The virtual work method is used to establish both governing differential equations and buckling equilibrium equations based on the first order shear deformation theory to include the effect of shear deformation for which analytical solutions for both limit point buckling and bifurcation point buckling are derived. A specific parameter that defines the switch between buckling and pre-buckling, limit point buckling and bifurcation buckling is proposed and defined. The effect of shear deformation on the buckling load is discussed in detail. It is observed from typical equilibrium paths of the arch that the shear deformation decreases the critical buckling load of laminated arches and this effect becomes more important and cannot be neglected for fixed arches with slenderness ratio S/rx < 150 and pinned arches with S/rx < 100. Direct comparisons with finite element results demonstrate that the proposed analytical solutions can provide a good prediction for the nonlinear buckling of shallow laminated arches under a uniform radial loading.