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.

Issue Section:
Brief Notes
Keywords:
functionally graded materials, Poisson ratio, Young's modulus, Galerkin method, bending, partial differential equations, internal stresses, Fourier series, Fourier analysis
Topics:
Fourier series, Functionally graded materials, Galerkin method, Poisson ratio, Stress, Young's modulus, Fourier analysis, Partial differential equations, Polynomials, Shear stress
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