Thermo-mechanical buckling of stepped circular bi-laminates

Abstract

Thermo-mechanical buckling of stepped circular bi-laminates subjected to a uniform temperature field is investigated analytically. The governing equations are derived via the Principal of Stationary Potential Energy, resulting in self-consistent constitutive equations of the composite structure, as well as the equations of motion and the associated matching and boundary conditions for the composite structure. A loading parameter is identified, and closed form analytical solutions to the non-linear problem are obtained, yielding exact results within the context of the formulation. A stability criterion is established based on the second variation of the total potential energy of the system in order to identify regions of stable and unstable equilibrium configurations, and a critical temperature and a critical membrane force are determined. Simulation results based on the analytical solutions are generated and a critical and characteristic behavior is assessed for both clamped-fixed supports and hinged-fixed supports conditions. The phenomenon of “sling-shot buckling” is observed. Results of parameter studies are also presented, which demonstrate the influence that material and geometric parameters of the system have on critical behavior. In particular, thermal expansion coefficient ratio, modulus ratio and thickness ratio all play a non-trivial role in the temperature carrying capacity of the structure for relatively large patches. Because the loading parameters and geometric parameters appear explicitly in the analytical solution and simulations, the model and results will be useful towards the design of micro-electromechanical systems, smart structures and related configurations.