Transient thermal stress analysis of a thin rotating FGM blade based on the exact shear correction factor: a comparison of ROM and LRVE homogenization models

Abstract

This work is an attempt to develop a simple and accurate finite element formulation based on first-order shear deformation theory (FSDT) for the transient thermal stress analysis of a pre-twisted and tapered thin rotating functionally graded material (FGM) blade, induced due to the thermal shock. The neutral surface of the FGM blade is taken as the reference plane and the exact shear correction factor is obtained from the equivalent energy principle. The temperature-dependent material property at a point in the thickness direction is estimated according to the rule of mixture (ROM) and the Local representative volume elements (LRVE) homogenization model. A finite element formulation using FSDT in conjunction with the eight-noded isoparametric element, taking five degrees of freedom is developed. The top layer of the thin FGM blade is subjected to a thermal shock and the bottom layer is kept at the ambient temperature. The governing equation for the present formulation is obtained using Hamilton’s principle. The accuracy of the present finite element formulation is established by comparing the results with the benchmark results. The parametric studies are conducted to investigate the effect of the angle of twist, variable chord and span, rotational speed, and accurate shear correction factor on the transient thermal stresses due to the thermal shock. Notably, there can be significant differences in the transient thermal stresses calculated by the two homogenization models viz., ROM and LRVE. Also, it is important to consider the exact shear correction factor in the formulation.