Time-dependent creep analysis of a functionally graded simple blade using first-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 defined so that one can define his own blade profile 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 field 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 differential equations of the problem are obtained using principle of virtual work as well as first order shear deformation theory. Coefficients of these differential equations are variable so by division method, these are solved and the distribution of stresses and displacements are presented for three different 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.

KEYWORDS:

• Simple blade
• functionally graded material
• time-dependent creep
• successive elastic solution
• first-order shear deformation theory (FSDT)

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the University of Kashan.