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Semi‐analytical far field model for three‐dimensional finite‐element analysis
Author(s) -
Doherty James P.,
Deeks Andrew J.
Publication year - 2004
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.380
Subject(s) - finite element method , stiffness matrix , mathematical analysis , discretization , boundary (topology) , mixed finite element method , boundary knot method , extended finite element method , boundary value problem , mathematics , method of fundamental solutions , matrix (chemical analysis) , displacement field , displacement (psychology) , boundary element method , geometry , structural engineering , engineering , materials science , psychology , composite material , psychotherapist
A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non‐linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three‐dimensional finite‐elements with the recently developed scaled boundary finite‐element method . The scaled boundary finite‐element method is a semi‐analytical technique based on finite‐elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co‐ordinate direction, but, unlike the boundary‐element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three‐dimensional finite‐element domain with the stiffness matrix of the unbounded scaled boundary finite‐element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd.