Thermo-mechanical stability analysis of FG composite beam-type structures with open thin-walled cross-sections considering temperature distributions

Abstract

This research investigates the stability behaviour of functionally graded (FG) thin-walled beam-type structures under thermo-mechanical loads. For this purpose, a geometrically nonlinear beam finite element formulation is introduced capable of modelling stability problems arising from varying temperature conditions. Uniform, linear, and nonlinear temperature distributions through the wall thickness are considered, respectively, and a linear distribution along the beam is also allowed. Temperature-dependent material properties are allowed using the power-law function. The equilibrium equations of the beam element are derived using the updated Lagrangian incremental formulation and the principle of virtual works. The small strain and large rotation conditions are assumed to be valid. Stress resultants are calculated by the Euler-Bernoulli-Navier and Vlasov theories for bending and torsion, respectively. On the basis of the aforementioned FG beam formulation, a computer program is developed. The program has capabilities to deal with both approaches, i.e. the eigenvalue and load-deformation ones, respectively. In the latter case, a small perturbation load need to be introduced along with the nominal load. By imposing different boundary conditions, power-law index values and FG distributions, the buckling temperature value as well as the nonlinear response of a beam-type structure under consideration can be determined. The obtained results are compared with those available from existing literature or obtained by the shell finite element model.