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Discrete gradient method in solid mechanics
Author(s) -
Lu Jia,
Qian Jing,
Han Weimin
Publication year - 2007
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.2187
Subject(s) - voronoi diagram , mathematics , boundary value problem , operator (biology) , elasticity (physics) , mathematical analysis , finite element method , geometry , physics , engineering , structural engineering , biochemistry , chemistry , repressor , transcription factor , gene , thermodynamics
A discrete method to boundary value problems in solid mechanics is presented. In this method, the unknown variable and its derivative are defined only at nodes. A discrete gradient operator is constructed with the aid of a tensorial identity on the Voronoi diagram. This operator is utilized in a weak form to derive a discrete Galerkin formulation for the boundary value problem. The theoretical underpins of the methodology are discussed, and the details of computational implementation in two‐dimensional elasticity, both small strain and finite strain, are provided. Several benchmark tests are presented to demonstrate the accuracy, convergence, and other properties of the method. Copyright © 2007 John Wiley & Sons, Ltd.