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Finite layer analysis of layered elastic materials using a flexibility approach. Part 1—Strip loadings
Author(s) -
Small J. C.,
Booker J. R.
Publication year - 1984
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.1620200606
Subject(s) - flexibility method , finite element method , stiffness matrix , direct stiffness method , compressibility , stiffness , flexibility (engineering) , layer (electronics) , matrix (chemical analysis) , structural engineering , displacement (psychology) , fourier series , mathematical analysis , mathematics , materials science , engineering , mechanics , physics , composite material , statistics , psychology , psychotherapist
It is well known that the analysis of a horizontally layered elastic material can be considerably simplified by the introduction of a Fourier or Hankel transform and the application of the finite layer approach. The conventional finite layer (and finite element) stiffness approach breaks down when applied to incompressible materials. In this paper these difficulties are overcome by the introduction of an exact finite layer flexibility matrix. This flexibility matrix can be assembled in much the same way as the stiffness matrix and does not suffer from the disadvantage of becoming infinite for an incompressible material. The method is illustrated by a series of examples drawn from the geotechnical area, where it is observed that many natural and man‐made deposits are horizontally layered and where it is necessary to consider incompressible behaviour for undrained conditions.