Analytical solution of stress and strain distributions in press fitted orthotropic cylinders

• The analytical solution of the macro mechanical model in orthotropic cylinders has been developed.
• The stress and the strain distributions produced by press fitted couplings have been evaluated.
• The macro mechanical model has been manipulated in function of the boundary conditions (pressures and forces).
• The proposed model enables to calculate the forces generated between the mating surfaces as well as the stress and strain distributions inside the cylinders.
• The theoretical results have been verified by some finite elements analyses.

This paper deals with the analytical solution of the macro mechanical model useful for evaluating the stress and the strain distributions produced by the press fit operation in orthotropic cylinders. The compliance and stiffness matrices have been rewritten in function of the radial coordinate after having integrated the differential equation of equilibrium. The boundary conditions (pressures and forces) were applied to the cylinder in order to calculate the integration constants and, then, to obtain the corresponding stress and strain equations. Finally the macro mechanical model has been manipulated in order to calculate both the coupling pressure and the stress and strain distributions inside two orthotropic cylinders press fitted with a stated value of interference level. The proposed model is, therefore, useful to calculate the friction forces generated between the mating surfaces, as well as the stress and strain distributions inside the cylinders as a function of the interference level and of loads applied to the coupling and free surfaces. The theoretical results presented and discussed have been verified by some finite elements analyses.