A novel numerical solution for a functionally graded hollow cylinder with arbitrary elastic property along the radial direction

This paper provides a solution for a functionally graded hollow cylinder by using a novel numerical solution technique. The cylinder has an arbitrary elastic property along the radial direction. The cylinder is divided into N layers. The assumed Young's modulus in radial direction is approximated by the many power functions along layers. For an individual layer, two undetermined constants are involved in the elastic solution. Those undetermined coefficients can be evaluated from the continuation condition along interfaces of layers and the boundary conditions at the inner surface and outer surface of cylinder. After evaluating those coefficients, the displacement and the stress states in the cylinder are determined accordingly. This paper provides a universal method for solving the problem of FGM cylinder for the case of the arbitrary Young's modulus E(r) along the radial direction. Several numerical examples are presented in the paper. The obtained result shows that the FGMs property has a significant influence to the stress distribution.

Automated summary

This paper provides a solution for a functionally graded hollow cylinder using a novel numerical solution technique, which involves approximating the Young's modulus along the radial direction and determining displacement and stress states using undetermined coefficients and conditions. The obtained results demonstrate the significant influence of the FGM property on stress distribution.