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Structural Engineering and Mechanics Volume 57, Number 5, March10 2016 , pages 823-835 DOI: https://doi.org/10.12989/sem.2016.57.5.823 |
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A unified method for stresses in FGM sphere with exponentially-varying properties |
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Kerimcan Celebi, Durmus Yarimpabuc and Ibrahim Keles
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| Abstract | ||
| 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. | ||
| Key Words | ||
| complementary functions method; thick sphere; functionally graded materials (FGMs); exponentially varying properties | ||
| Address | ||
| Kerimcan Celebi: Department of Mechanical Engineering, Adana Science and Technology University, Adana,Turkey Durmus Yarimpabuc: Department of Mathematics, Osmaniye Korkut Ata University, Osmaniye, Turkey Ibrahim Keles: Department of Mechanical Engineering, Ondokuz Mayis University, Samsun, Turkey | ||