Time-dependent creep analysis of a functionally graded beam with trapezoidal cross section using first-order shear deformation theory

Time-dependent creep analysis of a rotating functionally graded cantilever beam with trapezoidal longitudinal cross section subjected to thermal and inertia loading is investigated using first-order shear deformation theory (FSDT). The model described in this paper is a simple simulation of a turbine blade working under creep condition. The material is a metal based composite reinforced by a ceramic where the creep properties of which has been described by the Sherby\' s constitutive model. All mechanical and thermal properties except Poisson\'s ratio are assumed to be variable longitudinally based on the volume fraction of constituent. The principle of virtual work as well as first order shear deformation theory is used to derive governing equations. Longitudinal distribution of displacements and stresses are investigated for various volume fractions of reinforcement. Method of successive elastic solution is employed to obtain history of stresses and creep deformations. It is found that stresses and displacements approach their steady state values after 40000 hours. The results presented in this paper can be used for selection of appropriate longitudinal distribution of reinforcement to achieve the desired stresses and displacements.