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Abstract: This paper presents an analytical layer-element method used to analyze the displacement of a multi-layered transversely isotropic elastic medium of arbitrary depth subjected to axisymmetric loading. Based on the basic constitutive equations and the HU Hai-chang’s solutions for transversely isotropic elastic media, the state vectors of a multi-layered transversely isotropic medium were deduced. From the state vectors, an analytical layer element for a single layer (i.e., a symmetric and exact stiffness matrix) was acquired in the hankel transformed domain, which not only simplified the calculation but also improved the numerical efficiency and stability due to the absence of positive exponential functions. The global stiffness matrix was obtained by assembling the interrelated layer elements based on the principle of the finite layer method. By solving the algebraic equations of the global stiffness matrix which satisfy the boundary conditions, the solutions for multi-layered transversely isotropic media in the hankel transformed domain were obtained. The actual solutions of this problem in the physical domain were acquired by inverting the hankel transform. This paper presents numerical examples to verify the proposed solutions and investigate the influence of the properties of the multi-layered medium on the load-displacement response.

[1]Ai, Z.Y., Zeng, W.Z., 2011. Analytical layer-element method for non-axisymmetric consolidation of multilayered soils. International Journal for Numerical and Analytical Methods in Geomechanics, in press.

[2]Ai, Z.Y., Yue, Z.Q., Tham, L.G., Yang, M., 2002. Extended Sneddon and Muki solutions for multilayered elastic materials. International Journal of Engineering Science, 40(13):1453-1483.

[3]Ai, Z.Y., Cheng, Y.C., Zeng, W.Z., 2010. Analytical layer-element solution to axisymmetric consolidation of multilayered soils. Computers and Geotechnics, 38(2):227 232.

[4]Chen, G.J., Zhao, X.H., Yu, L., 1998. Transferring matrix method for solutions of non-axisymmetric load applied to layered cross-anisotropic elastic body. Chinese Journal of Geotechnical Engineering, 26(5):522-527 (in Chinese).

[5]Ding, H., Chen, W., Zhang, L., 2006. Elasticity of Transversely Isotropic Materials. Springer, the Netherlands.

[6]Hu, H.C., 1953. On the three-dimensional problems of the theory of elasticity of a transversely isotropic body. Acta Physica Sinica, 9(2):130-147 (in Chinese).

[7]Liao, J.J., Wang, C.D., 1998. Elastic solutions for a transversely isotropic half-space subjected a point load. International Journal for Numerical and Analytical Methods in Geomechanics, 22(6):425-447.

[8]Pan, E., 1989a. Static response of a transversely isotropic and layered half-space to general surface loads. Physics of the Earth and Planetary Interiors, 54(3-4):353-363.

[9]Pan, E., 1989b. Static response of a transversely isotropic and layered half-space to general dislocation sources. Physics of the Earth and Planetary Interiors, 58(2-3):103-117.

[10]Pan, E., 1997. Static Green’s functions in multilayered half-spaces. Applied Mathematical Modelling, 21(8):509-521.

[11]Pan, E., Yang, B., Cai, X., Yuan, F.G., 2001. Stress analyses around holes in composite laminates using boundary element method. Engineering Analysis with Boundary Elements, 25(1):31-40.

[12]Pan, Y.C., Chou, T.W., 1976. Point force solution for an infinite transversely isotropic solid. Journal of Applied Mechanics, 43(4):608-612.

[13]Pan, Y.C., Chou, T.W., 1979. Green’s function solutions for semi-infinite transversely isotropic materials. International Journal of Engineering Science, 17(5):545-551.

[14]Rahman, M., Newaz, G., 2000. Boussinesq type solution for a transversely isotropic half-space coated with a thin film. International Journal of Engineering Science, 38(7):807-822.

[15]Sneddon, I.N., 1972. The Use of Integral Transform. McGraw-Hill, New York.

[16]Wang, C.D., Liao, J.J., 1998. Stress influence chart for transversely isotropic rocks. International Journal of Rock Mechanics and Mining Sciences, 35(6):771-785.

[17]Wang, C.D., Liao, J.J., 1999. Elastic solutions for a transversely isotropic half-space subjected buried axisymmetric loads. International Journal for Numerical and Analytical Methods in Geomechanics, 23(2):115-139.

[18]Wang, C.D., Tzeng, C.S., Pan, E., Liao, J.J., 2003. Displacements and stresses due to a vertical point load in an inhomogeneous transversely isotropic half-space. International Journal of Rock Mechanics and Mining Sciences, 40(5):667-685.

[19]Wang, C.D., Pan, E., Tzeng, C.S., Han, F., Liao, J.J., 2006. Displacements and stresses due to a uniform vertical circular load in an inhomogeneous cross-anisotropic half-space. International Journal of Geomechanics, 6(1):1-10.

[20]Yu, H.Y., 2001. A concise treatment of indentation problems in transversely isotropic half-space. International Journal of Solids and Structures, 38(10-13):2213-2232.

[21]Yuan, F.G., Yang, S., Yang, B., 2003. Three-dimensional Green’s functions for composite laminates. International Journal of Solids and Structures, 40(2):331-342.

[22]Yue, Z.Q., 1995. Elastic fields in two joined transversely isotropic solids due to concentrated forces. International Journal of Engineering Science, 33(3):351-369.

[23]Yue, Z.Q., Xiao, H.T., Tham, L.G., Lee, C.F., Yin, J.H., 2005. Stresses and displacements of a transversely istropic elastic half-space due to rectangular loadings. Engineering Analysis with Boundary Elements, 29(6):647-671.