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| Bending analytic solutions of anisotropic rectangular plates with four free edges on the transversely isotropic elastic multilayered subgrade |
| Received:September 21, 2012 Revised:December 25, 2012 |
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| DOI：10.7511/jslx201401014 |
| KeyWord:transversely isotropic multilayered subgrade anisotropic rectangular thin plate with four free edges bending analytic solution |
| Author | Institution |
| 王春玲 |
西安建筑科技大学 理学院, 西安 |
| 丁欢 |
西安建筑科技大学 理学院, 西安 |
| 刘俊卿 |
西安建筑科技大学 理学院, 西安 |
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| Abstract: |
| In this paper,the bending solutions of anisotropic rectangular thin plate with four free edges on the transversely isotropic elastic multilayered subgrade were analyzed.First,based on Hu Haichang's theory and using Fourier transformation and transferring matrix method,both displacement and stress of the transversely isotropic elastic multilayered subgrade can be achieved.Then it combines the governing equation of bending of anisotropic rectangular thin plate with four free edges on the elastic foundation with deformation compatibility equation of the plate and foundation based on static integral transform solution of the displacement on the transversely isotropic elastic multilayered subgrade loaded with arbitrary vertical load.According to symmetrical decomposition and then using triangular series method,we obtained the analytical bending solution of anisotropic rectangular thin plate with four free edges on the transversely isotropic elastic multilayered subgrade.That is,the analytical expressions of the foundation reaction force,the deflection of the plate and the internal force of the plate were derived.It overcomes the drawbacks of the numerical method,cancels the assumptions of the ground reaction force,and avoids the calculation of the matrix exponential function; as well as considers the layer of the foundation and the difference between the plate and the foundation,so as to obtain more realistic distribution law of the internal force of the plate and the foundation reaction.The agreements between the numerical results and the literature results prove that the method in this paper is practical and achievable. |
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