NDLI: A higher-order theory for static and dynamic analyses of functionally graded beams

Content Provider	Springer Nature Link
Author	Li, Xian Fang Wang, Bao Lin Han, Jie Cai
Copyright Year	2010
Abstract	The higher-order theory is extended to functionally graded beams (FGBs) with continuously varying material properties. For FGBs with shear deformation taken into account, a single governing equation for an auxiliary function F is derived from the basic equations of elasticity. It can be used to deal with forced and free vibrations as well as static behaviors of FGBs. A general solution is constructed, and all physical quantities including transverse deflection, longitudinal warping, bending moment, shear force, and internal stresses can be represented in terms of the derivatives of F. The static solution can be determined for different end conditions. Explicit expressions for cantilever, simply supported, and clamped-clamped FGBs for typical loading cases are given. A comparison of the present static solution with existing elasticity solutions indicates that the method is simple and efficient. Moreover, the gradient variation of Young’s modulus and Poisson’s ratio may be arbitrary functions of the thickness direction. Functionally graded Rayleigh and Euler–Bernoulli beams are two special cases when the shear modulus is sufficiently high. Moreover, the classical Levinson beam theory is recovered from the present theory when the material constants are unchanged. Numerical computations are performed for a functionally graded cantilever beam with a gradient index obeying power law and the results are displayed graphically to show the effects of the gradient index on the deflection and stress distribution, indicating that both stresses and deflection are sensitive to the gradient variation of material properties.
Starting Page	1197
Ending Page	1212
Page Count	16
File Format	PDF
ISSN	09391533
Journal	Archive of Applied Mechanics
Volume Number	80
Issue Number	10
e-ISSN	14320681
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-05-08
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Dynamic governing equation Functionally graded material Higher-order beam theory Closed-form solution Mechanics Theoretical and Applied Mechanics
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering

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