In-plane buckling of flexibly bonded three-layer pinned-fixed half-sine shallow arches. (May 2023) - Adam, Christoph; Ladurner, Dominik; Furtmüller, Thomas
Abstract: In this paper, the nonlinear in-plane instability of symmetrically layered half-sine shallow arches with interlayer slip, which are soft-hinged supported on both ends, is studied. The equations of nonlinear equilibrium are derived with the principle of the minimum of total potential energy under the assumption that for each layer separately the kinematic hypotheses of the Euler–Bernoulli theory are valid. Based on these equations, analytical expressions for limit point buckling and bifurcation buckling are derived for a sine half-wave curved shallow arch subjected to a sine half-wave radial loading. In particular, closed-form solutions for the critical loads, the limit points, the bifurcation points, and the nonlinear pre- and post-buckling equilibrium paths are provided. To validate these relations, in two example problems the analytically obtained solutions are compared with the results of a finite element analysis with plane stress continuum elements, where the deflection and the interlayer slips in the pre- and post-buckling equilibrium path are examined. The derived relationships provide comprehensive insight into the in-plane (in-)stability of shallow arches with interlayer slip without the need for costly numerical parameter studies. Highlights: Equilibrium equations for stability analysis of shallow arches with interlayer slip. Analytical expressions for critical loads, pre- and post-buckling paths derived. Analytical solution verified through comparative plane stress FE analyses. First analytical solution of this problem. Significant impact of flexible bond of layers on critical loads highlighted.