The method of Fourier analysis is combined with the Galerkin method for solving the two-dimensional elasticity equations for a functionally graded beam subjected to transverse loads. The variation of the Young’s modulus through the thickness is given by a polynomial in the thickness coordinate and the Poisson’s ratio is assumed to be constant. The Fourier series method is used to reduce the partial differential equations to a pair of ordinary differential equations, which are solved using the Galerkin method. Results for bending stresses and transverse shear stresses in various beams show excellent agreement with available exact solutions. The method will be useful in analyzing functionally graded structures with arbitrary variation of properties.
A Combined Fourier Series–Galerkin Method for the Analysis of Functionally Graded Beams
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, July 1, 2002, final revision, December 5, 2003. Associate Editor: R. R. C. Benson.
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Zhu , H., and Sankar , B. V. (June 22, 2004). "A Combined Fourier Series–Galerkin Method for the Analysis of Functionally Graded Beams ." ASME. J. Appl. Mech. May 2004; 71(3): 421–424. https://doi.org/10.1115/1.1751184
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