Consistent infinitesimal finite-element cell method: in-plane motion

Abstract

To calculate the unit-impulse response matrix of an unbounded medium for use in a time-domain analysis of medium-structure interaction, the consistent infinitesimal finite-element cell method is developed. Its derivation is based on the finite-element formulation and on similarity. The limit of the cell width is performed analytically yielding a rigorous representation in the radial direction. The discretization is only performed on the structure-medium interface. Explicit expressions of the coefficient matrices for the in-plane motion of anisotropic material are specified, which depend only on the geometry of the structure-medium interface and the material properties of the unbounded medium. For each time step a linear system of equations is solved. The calculated unit-impulse response matrix is symmetric. In contrast to the boundary-element formulation, no fundamental solution is necessary and equilibrium and compatibility on the layer interfaces extending from the structure-medium interface to infinity, if present, are incorporated automatically. Excellent accuracy is achieved for an inhomogeneous semi-infinite wedge and a rectangular foundation embedded in an inhomogeneous half-plane.