Accurate numerical modeling for functionally graded (FG) cylinders of finite length subjected to thermo mechanical load

Abstract

A simplified and accurate analytical cum numerical model is presented here to investigate the behavior of FG cylinders of finite length subjected to thermo mechanical load. A diaphragm supported FG cylinder under symmetric thermal and mechanical load which is considered as a two dimensional (2D) plane strain problem of thermoelasticity in (r, z) direction. The boundary conditions are satisfied exactly in axial direction (z) by taking an analytical expression in terms of Fourier series expansion. Fundamental (basic) dependent variables are chosen in the radial coordinate of the cylinder. First order simultaneous ordinary differential equations are obtained as mathematical model which are integrated through an effective numerical integration technique by first transforming the BVP into a set of initial value problems (IVPs). For FG cylinders, the material properties have power law dependence in the radial coordinate. Effect of non homogeneity parameters on the stresses and displacements of FG cylinder are studied. The numerical results obtained are also first validated with existing literature for their accuracy. Stresses and displacements in axial and radial directions in cylinders having various l/rᵢ and rₒ/rᵢ ratios parameter are presented for future reference.