Consistent Infinitesimal Finite-Element–Cell Method: Out-of-Plane Motion

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 out-of-plane (antiplane) motion 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 the conditions on the boundaries extending from the structure-medium interface to infinity are incorporated automatically. Applications of the consistent infinitesimal finite-element–cell method to the semiinfinite wedge and the strip footing with rectangular cross section embedded in a half plane show excellent accuracy.