Time-dependent creep analysis of a functionally graded simple blade using fi rst-order shear deformation theory

Abstract

Thermo-elastic and history of stresses and displacements of a rotating functionally graded simple blade is studied using method of successive approximation and a variable thickness cantilever beam model. The rotating blade geometry and loading are mathematically de fi ned so that one can de fi ne his own blade pro fi le and loading using any particular function. The blade is subjected to a transverse distributed force, an inertia body force due to rotation and a distributed temperature fi eld due to a thermal gradient between the tip and the root. The creep behaviour is modelled by Sherby ’ s constitutive model. All mechanical and thermal properties except Poisson ’ s ratio are assumed to be longitudinally variable based on the volume fraction of reinforcement. The governing di ff erential equations of the problem are obtained using principle of virtual work as well as fi rst order shear deformation theory. Coe ffi cients of these di ff erential equations are variable so by division method, these are solved and the distribution of stresses and displacements are presented for three di ff erent volume content of reinforcement. By using Mendelson ’ s method of successive elastic solution, history of stresses and displacements are obtained. It has been found from history of stresses and displacements that they converge to their steady state condition almost after 50,000 hours.