Mechanical analysis of functionally graded beams

In this thesis, mechanical (statical and dynamical) analyses of functionally graded continuous systems are carried out by analytical, computational, and experimental methods. Analytical results are obtained by solving a partial differential equation, which is the equation of motion. Computational results are obtained utilizing Ansys Workbench (Ansys WB) software, and experimental results are obtained through tensile, bending, and modal analysis tests. The mathematical model of the functionally graded Euler-Bernoulli beam with power law function is constructed using Hamilton's Principle. Natural frequencies of the beam are achieved by solving the eigenvalue-eigenfunction problem, and mode shapes are obtained. Natural frequencies of the functionally graded beam are compared with studies in the literature. Computational analyses of the functionally graded beam are carried out using a novel modeling method using the finite element method by Ansys WB software. Results of the finite element analyses are compared with studies in the literature and analytical results. One directional functionally graded beam test specimens are manufactured by a three-dimensional printer, which is designed for this study. Using additive manufacturing, tensile, bending, and modal tests are carried out, and these results are compared with the results obtained by analytical and computational analyses. Finally, analyses are carried out to evaluate the achievement of the novel modeling method presented for the first time in this study on results of graded beams by different functions and under various loads and accuracy of the results given by studies in the literature.