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A new approach to boundary modelling for finite difference applications in solid mechanics
Author(s) -
Dow John O.,
Jones Michael S.,
Harwood Shawn A.
Publication year - 1990
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.1620300107
Subject(s) - finite element method , traction (geology) , finite difference , displacement (psychology) , polygon mesh , boundary value problem , mathematics , finite difference method , taylor series , mathematical analysis , geometry , structural engineering , engineering , mechanical engineering , psychology , psychotherapist
Procedures for extending the useful scope of the finite difference method in solid mechanics applications are presented. The improvements centre around the introduction of the physical nature of the deformations into the equations used to formulate the approximate solution. This is accomplished by evaluating the coefficients of Taylor series expansions for the displacement approximations in terms of rigid body motions, strains and derivatives of strains. This procedure is demonstrated with plane stress applications. The ability to interpret the derivative approximations physically allows the fictitious nodes typical of the finite difference method to be rationally incorporated into the model as a means of enforcing traction boundary conditions. An example problem is solved using both regular and irregular meshes. The displacements and stresses compare well with finite element solutions.