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Elastic wave propagation in unsaturated porous media using hybrid‐Trefftz stress elements
Author(s) -
Moldovan I.D.,
Cao T.D.,
Teixeira de Freitas J.A.
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4566
Subject(s) - finite element method , porous medium , stress (linguistics) , homogeneous , coupling (piping) , domain (mathematical analysis) , stress field , mathematics , mathematical analysis , mechanics , porosity , physics , structural engineering , engineering , geotechnical engineering , mechanical engineering , linguistics , philosophy , combinatorics
SUMMARY The stress model of the hybrid‐Trefftz finite element is formulated for the analysis of elastodynamic problems defined on unsaturated porous media. The supporting mathematical model is the theory of mixtures with interfaces and considers the full coupling between the solid, fluid and gas phases, including the effect of seepage acceleration. Hybrid‐Trefftz stress elements use the free‐field regular solutions of the homogeneous Navier (or Beltrami) equation to construct the approximation of the generalized stresses in the domain of the element. The influence of non‐homogeneous terms in the Navier equation is modelled using solutions of the corresponding static problem. The resulting elements are highly convergent under p‐ refinement and robust to both low and high excitation frequencies, as the trial functions embody relevant physical information on the modelled phenomenon. Copyright © 2013 John Wiley & Sons, Ltd.