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The economical solution of elastic problem for a range of Poisson's ratio
Author(s) -
Booker J. R.,
Small J. C.
Publication year - 1975
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.1620090406
Subject(s) - power series , poisson's ratio , mathematics , mathematical analysis , range (aeronautics) , series (stratigraphy) , poisson distribution , convergence (economics) , compressibility , zero (linguistics) , stiffness , materials science , physics , mechanics , thermodynamics , paleontology , linguistics , statistics , philosophy , economics , composite material , economic growth , biology
Abstract In this paper an economical method for calculating the stress and displacement fields in an elastic body for a range of Poission's ratios is given. The solution is expanded as a power series in Poission's ratio, the coefficients of the series being determined successively. The range of convergence of the solution is examined, and it is shown that the power series converges for values of Poission's ratio in the range zero to a half, provided a suitable point of expansion is chosen. Particular features of the method are firstly that only one effective inversion of the stiffness matrix, for Poission's ratio zero, is required to obtain the solution for all Poission's ratio and secondly that no special formulation for an incompressible material is required.