Buckling and post-buckling analysis of three-layer shallow arches with geometric imperfections and interlayer slip

Abstract

In this paper, a semi-analytical solution is derived to capture the nonlinear stability and equilibria of shallow three-layered arches with flexible bond, which also accounts for the interlayer slip (i.e., the relative displacement between the layers). The member axis can have arbitrary geometric imperfections. With the equations presented, for the first time, the complete stable and unstable equilibrium paths can be predicted including multiple remote equilibria, which may occur in the presence of an imperfect member axis but cannot be determined with finite element simulations. Expressions for the direct prediction of critical loads for limit point buckling and bifurcation buckling are also provided, which may also be on the remote unconnected equilibrium paths. In several application examples, the effect of geometric imperfection and interlayer slip on the critical loads and nonlinear equilibria is revealed. Comparative finite element analyses with plane stress continuum elements demonstrate the accuracy and computational efficiency of the presented theory.