Mechanical Behavior and Optimization of Functionally Graded Hollow Cylinder with an Elliptic Hole

This paper presents a numerical solution and optimization for a functionally graded material cylinder with an elliptic hole subjected to mechanical pressure. To obtain the governing equations, an elliptic cylindrical coordinate was used. The material properties were considered in a way in order to vary with power-law function along the elliptic cylindrical direction. The differential quadrature method was used for solving the equations. In addition, by using von-Mises stress along with the thickness, the optimal values for various material inhomogeneity and the geometry of the cylinder investigated. The results showed that the inconsistency in shape of the hole in the cylindrical vessel can affect the expected results and the stresses in thickness of cylinder were changed. Furthermore, it was shown that with low values of the functionally graded material index, the geometry of the cylinder had a more significant effect on von Misses stress. Additionally, with high values for the material index, the values for von Misses stress converged together and the material inhomogeneity had a less noticeable effect on stress. The results also showed that for various geometries of the cylinder and holes, the best value for material homogeneity to reach the optimum value for von Misses stress was changed. The presented results were consistent with those reported in previous publications.