Analytical layer-element solutions for a multi-layered transversely isotropic elastic medium subjected to axisymmetric loading

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.