A Dirichlet-to-Neumann finite element method for axisymmetric elastostatics in a semi-infinite domain
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Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Abstract
The Dirichlet-to-Neumann finite element method (DtN FEM) has proven to be a powerful numerical approach to solve boundary-value problems formulated in exterior domains. However, its application to elastic semi-infinite domains, which frequently arise in geophysical applications, has been rather limited, mainly due to the lack of explicit closed-form expressions for the DtN map. In this paper, we present a DtN FEM procedure for boundary-value problems of elastostatics in semi-infinite domains with axisymmetry about the vertical axis. A semi-spherical artificial boundary is used to truncate the semi-infinite domain and to obtain a bounded computational domain, where a FEM scheme is employed. By using a semi-analytical procedure of solution in the unbounded residual domain lying outside the artificial boundary, the exact nonlocal boundary conditions provided by the DtN map are numerically approximated and efficiently coupled with the FEM scheme. Numerical results are provided to demonstrate the effectiveness and accuracy of the proposed method. (C) 2016 Elsevier Inc. All rights reserved.
Description
Keywords
Dirichlet-to-Neumann map, Semi-infinite domain, Finite elements, Elasticity, NONREFLECTING BOUNDARY-CONDITIONS, EXTERIOR SCATTERING PROBLEMS, INFINITE ELASTIC-FOUNDATION, DTN-FE METHOD, ARTIFICIAL BOUNDARY, UNBOUNDED-DOMAINS, ERROR ANALYSIS, WAVE-EQUATION, APPROXIMATION