Discrete gradient method in solid mechanics

Jia Lu; Jing Qian; Weimin Han

doi:10.1002/nme.2187

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Discrete gradient method in solid mechanics

Journal article

Peer reviewed

Discrete gradient method in solid mechanics

Jia Lu, Jing Qian and Weimin Han

International Journal for Numerical Methods in Engineering, Vol.74(4), pp.619-641

04/23/2008

DOI: 10.1002/nme.2187

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Abstract

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.

Voronoi diagram

meshless methods

discrete gradient

discrete methods

Galerkin methods

Details

Title: Subtitle: Discrete gradient method in solid mechanics
Creators: Jia Lu
Jing Qian
Weimin Han
Resource Type: Journal article
Publication Details: International Journal for Numerical Methods in Engineering, Vol.74(4), pp.619-641
DOI: 10.1002/nme.2187
ISSN: 0029-5981
eISSN: 1097-0207
Publisher: John Wiley & Sons, Ltd; Chichester, UK
Number of pages: 23
Grant note: National Science Foundation (CMS 03‐48194)
Language: English
Date published: 04/23/2008
Academic Unit: Mathematics; Mechanical Engineering
Record Identifier: 9983985835502771

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