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A generalized finite difference method for solid mechanics
Author(s) -
Dow John O.,
Jones Michael S.,
Harwood Shawn A.
Publication year - 1990
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690060204
Subject(s) - finite element method , mathematics , traction (geology) , generalization , finite difference , boundary value problem , finite difference method , plane stress , taylor series , boundary (topology) , mathematical analysis , calculus (dental) , structural engineering , engineering , mechanical engineering , medicine , dentistry
Procedures are developed that improve the applicability of the finite difference method to problems in solid mechanics. This is accomplished by formulating the coefficients of the Taylor series expansion used to approximate derivative quantities in terms of physically interpretable strain gradients. Improvements realized include modeling of boundary conditions that has intuitive appeal and the use of irregular grids in a natural manner. These developments are demonstrated for the analysis of plane stress problems with traction boundary conditions. The results compare well with finite element solutions. The approach suggests further generalization of the finite difference method.