Deformation analysis of functionally graded variable cross-section rod

The deformation analysis of a functionally graded rod with a variable cross-sectional area in the axial direction is considered. Material properties such as elastic modulus and density are assumed to be graded in the axial direction. These conditions result in a partial differential equation with variable coefficients that is difficult to solve with traditional analytical methods. Using the Laplace transform, the partial differential equation is transformed into a time-independent boundary value problem in the axial direction and solved using the pseudospectral Chebyshev method. Displacements in physical space are obtained using the modified inverse Durbin method. The results obtained with the combined numerical method are validated with literature. The effects of randomly generated cross-sectional planes and the material mixture on the displacement distributions are discussed. Key Words: Deformation Analysis, Functionally Graded Rods, Pseudospectral Chebyshev Method, Laplace Transform, Modified Durbin Method