Numerical Characterization of Stress Distribution in Exponentially Graded Pressurized Cylinders Incorporating Metal-Ceramic Combinations

In this study, we have developed a comprehensive model for computation of stresses in an axisymmetric cylinder graded with material properties in an exponential form, under a plain strain condition and subjected to compressive internal--external pressure. By integrating Navier's equilibrium equation together with Hooke's law and strain - displacement relation, the model investigates steady state elastic stress distribution in an axisymmetric pressurized functionally graded cylinder under three different material combinations, namely, $SUS304 - ZrO_{2}$, $CA - AlN$ and $HCS - MgO$. The material property, namely, stiffness, widely termed as Young's modulus is tailored exponentially at radial points across the cylinder, representing the functionally graded nature, used to optimize the stress distribution. Further, the numerical characterization of stress distribution in FG cylinder for all three above discussed materials is presented. The consequence of material property control parameter on the primary variable representing the field of displacement and the secondary variable representing stress field in the graded cylindrical body for three different material combinations is highlighted. The stability and convergence of solution obtained using Frobenius series solution method is presented with different number of terms considered in the series solution where it has been observed that the solution starts to converge after considering 10 terms. The outcome of error analysis for method of iteration, FEM and Frobenius series solution validates an excellent consistency between the obtained results. The implemented iterative technique shows an efficient convergence to the solution in just two iterations. Results of displacement and stresses are graphically presented and their appropriate contextual interpretation is discussed for understanding the efficacy of three methods for all the three material combinations. The obtained results are analysed thoroughly with critical viewpoint and the relative advantage of each solution method is presented.