Analytical and numerical axisymmetric elastic stress analyses of stationary/rotating discs made of isotropic/orthotropic functionally graded materials by the transfer matrix method

In this work, an elastic analysis of non-uniform discs made of nonhomogeneous radially functionally graded (FG) isotropic/orthotropic materials are studied numerically via the Transfer Matrix method (TMM). The Complementary Functions (CFM) method is originally employed for the determination of the overall transfer matrix of FG discs. CFM is also directly and independently applied to the solution of the same problems to test the TMM's results. To verify the numerical results, an exact analysis is also performed. Apart from those diverse material grading patterns, disc profiles, boundary conditions, and recent material-ceramic pairs are all considered at various constant angular velocities. All the solutions obtained by TMM are certainly original and a novel contribution to the literature. An elasticity solutions to orthotropic FGM disc with/without varying thickness; the constraint in the form that a rigid shaft at the center and a rigid casing at the outer for all types of materials; the parabolic-convex, linear and hyperbolic disc profiles for isotropic/orthotropic nonhomogeneous FG materials are also originally studied by CFM. Additionally such comprehensive compact formulas developed, in which all effects of the inner/outer pressures together with the rotation for discs made of all types of materials under different constraints, do not exist in the literature. As a conclusion, this study is original under all circumstantial conditions.