TIME-DOMAIN MODELS FORWAVE PROPAGATION IN UNBOUNDED DOMAINS BASED ON THE SCALED BOUNDARY FINITE ELEMENT METHOD AND A RATIONAL STIFFNESS APPROXIMATION

摘要

The paper is devoted to time-domain analyses of dynamic problems in unbounded domains. The scaled boundary finite element method (SBFEM) is particularly suited for this purpose, but formulated in the frequency-domain originally. The mixed-variables technique is used for the transformation of SBFE dynamic stiffness formulations into the time-domain. Here, a set of discrete dynamic stiffness matrices S~ (ω_j) is approximated by a rational function of iω using a least-squares approach. The resulting rational force-displacement relationship in the frequencydomain corresponds to a system of first-order differential equations in the time-domain, which can be coupled to the equations of motion of the near field and solved using standard timediscretization schemes. The strategy is demonstrated for two-dimensional problems, considering both a semi-infinite soil layer and an elastic foundation embedded in a half-plane.