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Elasticity Solution of Simply-supported Functionally Graded Beams with Variable Thickness


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Elasticity Solution of Simply-supported Functionally Graded Beams with Variable Thickness
XU Ye-peng1ZHOU Ding2
1.School of Sciences,NUST,Nanjing 210094,China;2.College of Civil Engineering,Nanjing University of Technology,Nanjing 210009,China
beams functionally graded materials variable thickness Fourier expansion elasticity solutions
In this paper,the Young’s modulus is graded through the thickness following the exponential-law and the Poisson’s ratio keeps constant.According to the governing equations of plane stress problems,the general expressions of displacements,which exactly satisfy the governing differential equations and the simply-supported boundary conditions at two ends of the beam,are deduced.The unknown coefficients in the solution are determined by using the Fourier sinusoidal series expansion to the boundary equations on the upper and lower surfaces of the beams.The excellent convergence of the solution is demonstrated.The results are accurately up to the third significant digit.The effect of the Young’s modulus varying rules on the displacements and stresses of functionally graded beams is investigated.The proposed elasticity solution can be used to assess the validity of various approximate solutions and numerical methods for functionally graded beams.It is applicable in aerospace engineering and other projects with highly accurate demand on stress analysis such as the design of micro-mechanical apparatus.


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Last Update: 2012-11-19