Analysis of functionally graded beams with variable thickness using first-order shear deformation theory subjected to mechanical and thermal loads

In this research, thermoelastic analysis of the beams with variable thickness made of functionally graded materials (FGM) has been carried out. The beam geometry is similar to a turbine blade. Loading is composed of a transverse distributed force, a specific temperature field and an inertia body force due to rotation. Tip of the beam is free and root of the beam is fixed. Mechanical and thermal properties are assumed to be variable along the longitudinal direction of the beam based on the power law variation. Using first-order shear deformation theory, linear strain–displacement relations and Generalized Hooke’s law, a system of second order differential equation is obtained. Using division method, differential equations are solved. For each division, longitudinal and transverse deflections and longitudinal, shear and effective stresses are obtained. For six different nonhomogeneous distributions, analyses were carried out based on the power law variation. The results show that beam made of FGM with positive and further index of non homogeneity, maximum longitudinal and transverse deflections and longitudinal, shear and effective stresses would be less.