Nonlinear analysis of bending, thermal buckling and post-buckling for functionally graded tubes by using a refined beam theory

Nonlinear bending, thermal buckling and post-buckling analysis for functionally graded materials (FGMs) tubes with two clamped ends by using a refined beam theory are investigated. The theory satisfies the traction-free boundary conditions on the inner and outer surfaces of the tube and also takes into account the transverse shear effects without artificially introducing shear correction factors. The material properties of FGM tubes are assumed to be temperature-dependent and vary in the radial direction. The asymptotic solutions of the FGM tubes under nonlinear bending and thermal post-buckling are solved by using a two-step perturbation method. The analytical solutions of Timoshenko beam and Euler beam are also presented. Detailed parametric studies are performed to investigate effects of inner-to-outer radius ratio, volume fraction as well as shear deformation on nonlinear bending, thermal buckling and post-buckling characteristics of the FGM tubes.