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    A NOVEL APPROACH TO THERMAL AND MECHANICAL STRESSES IN A FGM CYLINDER WITH EXPONENTIALLY-VARYING PROPERTIES
    (Polish Soc Theoretical & Applied Mechanics, 2017) Celebi, Kerimcan; Yarimpabuc, Durmus; Keles, Ibrahim
    A novel approach is employed to a general solution for one-dimensional steady-state thermal and mechanical stresses in a hollow thick cylinder made of a functionally graded material (FGM). The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the cylinder. The material properties, except Poisson's ratio, are assumed to be exponentially-varying through the thickness. Forcing functions applied to the inner boundary are internal pressures which may be in form of steps. These conditions result in governing differential equations with variable coefficients. Analytical solutions to such equations cannot be obtained except for certain simple grading functions and pressures. Numerical approaches must be adopted to solve the problem in hand. The novelty of the present study lies in the fact that the Complementary Functions Method (CFM) is employed in the analysis. The Complementary Functions method (CFM) will be infused into the analysis to convert the problem into an initial-value problem which can be solved accurately. Benchmark solutions available in the literature are used to validate the results and to observe the convergence of the numerical solutions. The solution procedure is well-structured, simple and efficient and it can be readily applied to cylinders. It is also well suited for problems in which mechanical properties are graded.
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    Öğe
    A unified method for stresses in FGM sphere with exponentially-varying properties
    (Techno-Press, 2016) Celebi, Kerimcan; Yarimpabuc, Durmus; Keles, Ibrahim
    Using the Complementary Functions Method (CFM), a general solution for the one-dimensional steady-state thermal and mechanical stresses in a hollow thick sphere made of functionally graded material (FGM) is presented. The mechanical properties are assumed to obey the exponential variations in the radial direction, and the Poisson's ratio is assumed to be constant, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the sphere. In the present paper, a semi-analytical iterative technique, one of the most efficient unified method, is employed to solve the heat conduction equation and the Navier equation. For different values of inhomogeneity constant, distributions of radial displacement, radial stress, circumferential stress, and effective stress, as a function of radial direction, are obtained. Various material models from the literature are used and corresponding temperature distributions and stress distributions are computed. Verification of the proposed method is done using benchmark solutions available in the literature for some special cases and virtually exact results are obtained.
  • [ X ]
    Öğe
    Free vibration analysis of functionally graded beams using complementary functions method
    (Springer, 2018) Celebi, Kerimcan; Yarimpabuc, Durmus; Tutuncu, Naki
    A novel approach is employed in the free vibration analysis of simply supported functionally graded beams. Modulus of elasticity, density of material, and Poisson's ratio may change arbitrarily in the thickness direction. The equations of motion are derived using the plane elasticity theory. The governing differential equations have variable coefficients, which are functions of material properties. Analytical solutions of such equations are limited to specific material properties. Hence, numerical approaches must be adopted to solve the problem on hand. The complementary functions method will be infused into the analysis to convert the problem into an initial-value problem which can be solved accurately. Solutions thus obtained are compared to closed-form benchmark solutions available in the literature and finite element software solutions to validate the method presented. Subsequently, it is demonstrated that the method is efficiently applicable to material properties changing arbitrarily through the thickness with continuous derivatives.