Dynamic, stability and static analyses of functionally graded and layered composite beams

The functionally graded composite materials are new type composite materials produced for correcting the negative features of layered composite materials. The stress concentrations in the interfaces of layered composite materials cause delamination and cracks between the laminations. To minimize this stress discontinuity caused by the prompt transition among the laminations, the stress concentrations are minimized by gradually grading the material features with the functionally graded materials. In this study, the comparative analysis of layered composite and functionally graded composite beams is performed. The composite materials are considered for a cantilever beam and their static, stability and dynamic responses are achieved and compared. In static analysis, a single load is applied at the end of each composite cantilever beam and static displacements and stresses are obtained. In stability analysis, a point pressure force is applied at the free end of cantilever beam and critical buckling loads are obtained and compared for each composite type. In dynamic analysis, vibration responses forced under a harmonic load are obtained and compared with the natural frequency of the two composite beams. The feature of the functionally graded materials changes according to a function through the thickness of the beam. The Euler-Bernoulli Beam Theory and Timoshenko Beam Theory are used for the beam model. Energy based Ritz method is used for solving the problem and the algebraic polynomials are represented with the test functions in the Ritz method. For solving the problem, the codes and algorithms are written in MATLAB program; the numerical results are achieved and the graphics of the analysis are drawn. In analyzing the static behavior, the effect of the material distribution and ratio of the length/height of the functionally graded beams on the static displacements and stress distribution is analyzed and compared with the static results of the layered composites. In stability analysis, an eigenvalue problem is created and the critical buckling load of the functionally graded beam is calculated and compared with the layered case. In vibration behavior analysis, the governing equations of the problem are achieved by using Lagrange procedure. Eigenvalue procedure is used for achieving free vibration results. For solving the forced vibration, the Newmark average acceleration method is used in the time definition slot. For forced vibration analysis, the damping affect is also considered with Kelvin-Voigt viscoelastic model. The effects of material distribution parameters and dynamic parameters on the natural frequency and forced vibration responses of functionally graded beams are achieved and the results are compared with the results of layered composites. The results obtained with MATLAB program are both compared with the particular results of the relevant studies in literature and with the results obtained by using ANSYS software, which showed that the data are coherent when compared with each other.