Geers, Thomas L.; Lewis, Brett A. Doubly asymptotic approximations for transient elastodynamics. (English) Zbl 0944.74570 Int. J. Solids Struct. 34, No. 11, 1293-1305 (1997). Summary: A doubly asymptotic approximation (DAA) is an approximate temporal impedance relation at the boundary of a continuous medium; it approaches exactness at both early and late times, effecting a smooth transition between. Here, first- and second-order DAAs are derived for a uniform, isotropic, elastic medium of either infinite or semi-infinite extent. The derivations proceed from pertinent singly asymptotic approximations and employ the method of operator matching previously used for acoustic domains. A simple problem with spherical symmetry is considered that illustrates the characteristics of the singly and doubly asymptotic approximations. Cited in 4 Documents MSC: 74J10 Bulk waves in solid mechanics 74S30 Other numerical methods in solid mechanics (MSC2010) PDFBibTeX XMLCite \textit{T. L. Geers} and \textit{B. A. Lewis}, Int. J. Solids Struct. 34, No. 11, 1293--1305 (1997; Zbl 0944.74570) Full Text: DOI