Nonlinear thermal dynamic buckling of FGM beams

Based on the nonlinear dynamic analysis, dynamic buckling and imperfection sensitivity of the FGM Timoshenko beam subjected to sudden uniform temperature rise are studied. Initial geometric imperfection of the beam is also taken into account. It is assumed that during deformation the beam is resting over a conventional three-parameter elastic foundation with softening/hardening cubic non-linearity. The analysis is performed with considering temperature dependency assumption of each thermomechanical property of the FGM beam. The governing nonlinear dynamic equations are derived based on the generalized Hamilton principle. In the spatial approximation of the problem, a set of ordinary differential equations in time is obtained by the conventional multi-term Ritz method. These equations are converted into a set of algebraic equations by utilizing the Newmark family of time approximation scheme. The obtained non-linear algebraic equations are solved via the well known Newton-Raphson iterative scheme. The Budiansky Roth criterion is used to detect the unbounded motion type of dynamic buckling. Results reveal that for beams with stable post-buckling equilibrium path, no dynamic buckling occurs according to the Budiansky Roth criterion. However, dynamic buckling may occur for the FGM beams resting on sufficiently stiff softening elastic foundation due to their unstable post-buckling equilibrium paths. (C) 2015 Elsevier Masson SAS. All rights reserved.