A Doubly Asymptotic, Nonreflecting Boundary for Ground-Shock Analysis

This paper desribes the formulation and implementation of a nonreflecting boundary for use with existing finite-element codes to perform nonlinear ground-shock analyses of buried structures. The boundary is based on a first-order doubly asymptotic approximation (DAA₁) for disturbances propagating outward from a selected portion of the soil medium surrounding the structure of interest. The resulting set of first-order ordinary differential equations is then combined with the second-order equations of motion for the finite-element model so as to facilitate solution by a staggered solution procedure. This procedure is shown to be computationally stable as long as the time increment is smaller than a limiting value based on the finite-element mass matrix and the DAA-boundary stiffness matrix. Computational results produced by the boundary are compared with exact results for linear canonical problems pertaining to infinite-cylindrical and spherical shells.