JZUS - Journal of Zhejiang University SCIENCE

Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.2 P.126-131

http://doi.org/10.1631/jzus.2005.A0126

The analytical solutions for orthotropic cantilever beams (I): Subjected to surface forces*

Author(s): Ai-min Jiang^1,2, Hao-jiang Ding¹
Affiliation(s): 1. Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China; more
Corresponding email(s): jam@vip.sina.com
Key Words: General solution, Orthotropic media, Cantilever beams, Analytical solutions

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Abstract: This paper first gives the general solution of two-dimensional orthotropic media expressed with two harmonic displacement functions by using the governing equations. Then, based on the general solution in the case of distinct eigenvalues, a series of beam problems, including the problem of cantilever beam under uniform loads, cantilever beam with axial load and bending moment at the free end, cantilever beam under the first, second, third and fourth power of x tangential loads, is solved by the superposition principle and the trial-and-error methods.

References

[1] Ding, H.J., Wang, G.Q., Chen, W.Q., 1997. General solution of plane problem of piezoelectric media expressed by “harmonic functions”. , Applied Mathematics and Mechanics. 18:757-764, :

[2] Ding, H.J., Wang, G.Q., Chen, W.Q., 1997. Green’s functions for a two-phase infinite piezoelectric plane. Proceedings of Royal Society of London (A), 453:2241-57.

[3] Lekhnitskii, S.G., 1969. Anisotropic Plate. , Gordon and Breach, London, :

[4] Timoshenko, S.P., Goodier, J.N., 1970. Theory of Elasticity (3rd Ed), McGraw Hill, New York,:

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