Analytical layer-element solutions for a multi-layered transversely isotropic elastic medium subjected to axisymmetric loading |
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Authors: | Zhi-yong Ai Nai-rui Cang and Jie Han |
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Institution: | [1]Key Laboratory of Geotechnical and Underground Engineering of MOE, Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China [2]Department of Ciwl, Environmental, and Architectural Engineering, The University of Kansas, Lawrence, KS 66045, USA |
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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. |
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