On the influence of edge damage on thermally induced buckling of stepped circular bi-laminates

Abstract

The influence of edge damage on thermo-mechanical buckling of stepped circular bi-laminates is examined analytically. The nonlinear equations of equilibrium, the associated boundary conditions and the transversality conditions for the propagating interior boundaries of a region of sliding contact are derived via the Principal of Stationary Potential Energy as a propagating boundary problem in the calculus of variations. The problem is ultimately recast in a mixed formulation expressed in terms of the membrane forces and the transverse displacements of the composite structure. A loading parameter is identified and closed form analytical solutions to the resulting non-linear problem are determined. In addition, a stability criterion is established based on the second variation of the total potential energy of the structure, and qualitative behavior concerning contact is deduced analytically. Results of numerical simulations based on the analytical solutions established herein are generated and the phenomenon of “sling-shot buckling” is observed, whereby the structure first deflects in one direction upon heating (or cooling) and then, when a critical temperature is achieved, dynamically “sling-shots” from the current equilibrium configuration to an alternate equilibrium configuration possessing deflections in the opposite sense. In addition, the phenomenon of “buckle-trapping” is observed for stepped circular bi-laminates with hinged-fixed supports, as well as for clamped-fixed structures with relatively large damaged area. A robust mixture of contact behavior, including propagating sliding contact, edge contact and no contact, and the transition from one form of contact to another, is exhibited for both pre-buckling and post-buckling configurations. The influence of edge damage on critical load and characteristic behavior is assessed.