Similar articles

Abstract: The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In the symplectic space, elasticity problems can be solved using the method of separation of variables along with the eigenfunction expansion technique, as in traditional Fourier analysis. The eigensolutions include those corresponding to zero and nonzero eigenvalues. The latter group can be further divided into α- and β-sets. This paper reformulates the form of β-set eigensolutions to achieve the stability of numerical calculation, which is very important to obtain accurate results within the symplectic frame. An example is finally given and numerical results are compared and discussed.

[1] Barber, J.R., 1992. Elasticity. Kluwer, Dordrecht.

[2] Ding, H.J., Chen, W.Q., Zhang, L.C., 2006. Elasticity of Transversely Isotropic Materials. Springer, Dordrecht.

[3] Ding, H.J., Huang, D.J., Chen, W.Q., 2007. Elasticity solutions for plane anisotropic functionally graded beams. International Journal of Solids and Structures, 44(1):176-196.

[4] Gu, Q., Xu, X.S., Leung, A.Y.T., 2005. Application of Hamiltonian system for two-dimensional transversely isotropic piezoelectric media. Journal of Zhejiang University SCIENCE A, 6(9):915-921.

[5] Huang, D.J., Ding, H.J., Chen, W.Q., 2007. Analytical solution for functionally graded anisotropic cantilever. Journal of Zhejiang University SCIENCE A, 8(9):1351-1355.

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

[7] Kameswara Rao, N.S.V., Das, Y.C., 1977. A mixed method in elasticity. Journal of Applied Mechanics, 44:51-56.

[8] Leung, A.Y.T., 1988. Integration of beam functions. Computers & Structures, 29(6):1087-1094.

[9] Leung, A.Y.T., 1990. Recurrent integration of beam functions. Computers & Structures, 37(3):277-282.

[10] Leung, A.Y.T., Zheng, J.J., 2007. Closed form stress distribution in 2D elasticity for all boundary conditions. Applied Mathematics and Mechanics, 28(12):1629-1642.

[11] Pestel, E.C., Leckie, F.A., 1963. Matrix Methods in Elasto Mechanics. McGraw-Hill, New York.

[12] Stephen, N.G., 2004. State space elastostatics of prismatic structures. International Journal of Mechanical Sciences, 46(9):1327-1347.

[13] Stephen, N.G., 2006. Transfer matrix analysis of the elastostatics of one-dimensional repetitive structures. Proceedings of the Royal Society of London, 462:2245-2270.

[14] Stephen, N.G., Ghosh, S., 2005. Eigenanalysis and continuum modelling of a curved repetitive beam-like structure. International Journal of Mechanical Sciences, 47(12):1854-1873.

[15] Stephen, N.G., Zhang, Y., 2006. Eigenanalysis and continuum modeling of pre-twisted repetitive beam-like structures. International Journal of Solids and Structure, 43(13):3832-3855.

[16] Timoshenko, S.P., Goodier, J.N., 1970. Theory of Elasticity. McGraw-Hill, New York.

[17] Xu, X.S., Gu, Q., Leung, A.Y.T., Zheng, J.J., 2005. A symplectic eigensolution method in transversely isotropic piezoelectric cylindrical media. Journal of Zhejiang University SCIENCE A, 6(9):922-927.

[18] Zhong, W.X., 1995. A New Systematic Methodology for Theory of Elasticity. Publishing House of Dalian University of Technology, Dalian (in Chinese).

[19] Zhong, W.X., Yao, W.A., 2002. Symplectic Elasticity. Higher Education Press, Beijing (in Chinese).