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Received: 2004-10-20

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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.3 P.155~158

http://doi.org/10.1631/jzus.2005.A0155


The analytical solutions for orthotropic cantilever beams (II): Solutions for density functionally graded beams


Author(s):  JIANG Ai-min, DING Hao-jiang

Affiliation(s):  Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   jam@vip.sina.com

Key Words:  General solution, Functionally graded media, Analytical solutions, Cantilever beams


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JIANG Ai-min, DING Hao-jiang. The analytical solutions for orthotropic cantilever beams (II): Solutions for density functionally graded beams[J]. Journal of Zhejiang University Science A, 2005, 6(3): 155~158.

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T1 - The analytical solutions for orthotropic cantilever beams (II): Solutions for density functionally graded beams
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Abstract: 
In this paper, the specific solutions of orthotropic plane problems with body forces are derived. Then, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally graded orthotropic media, a series of beam problem, including the problems of cantilever beam with body forces depending only on z or on x coordinate and expressed by z or x polynomial is solved by the principle of superposition and the trial-and-error method.

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Reference

[1] Anderson, T.A., 2003. A 3D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere. Composite Structures, 60:265-274.

[2] Jiang, A.M., Ding, H.J., 2005. The analytical solutions for orthotropic cantilever beams (I): Subjected to surface forces. Journal of Zhejiang University SCIENCE, 6A(2):126-131.

[3] Sankar, B.V., 2001. An elasticity solution for functionally graded beams. Composites Science and Technology, 61:689-696.

[4] Tutuncu, N., Ozturk, M., 2001. Exact solutions for stress in functionally graded pressure vessels. Composites: Part B, 32:683-686.

[5] Wu, C.H., Tsai, Y.H., 2004. Asymptotic DQ solutions of functionally graded annular spherical shells. European Journal of Mechanics A/Solids, 23:283-299.

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