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High‐order three‐dimensional discontinuous deformation analysis (3‐D DDA)
Author(s) -
Beyabanaki S. Amir Reza,
Jafari Ahmad,
Yeung M. Ronald
Publication year - 2010
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1220
Subject(s) - discontinuous deformation analysis , nonlinear system , displacement (psychology) , fictitious force , stiffness , deformation (meteorology) , stress (linguistics) , shear (geology) , structural engineering , function (biology) , mechanics , mathematics , mathematical analysis , physics , engineering , materials science , finite element method , psychology , linguistics , philosophy , quantum mechanics , meteorology , composite material , psychotherapist , evolutionary biology , biology
Three‐dimensional discontinuous deformation analysis (3‐D DDA) with high‐order displacement functions has been derived for the requirement of highly accurate stress and strain calculations. The high‐order displacement function allows nonlinear distributions of stresses and strains within a discrete block, which significantly enhances 3‐D DDA as an analysis technique. Formulations of stiffness and force matrices in second‐ and third‐order 3‐D DDA due to elastic stress, initial stress, body force, point load, fixed point, inertial force, normal and shear contact forces and friction force are presented. The VC++ codes for the second‐ and third‐order cases have been developed, and they have been applied to examples of 3‐D beams, bending under various loading conditions applied at the end and to an example of discontinuous problem. Results of modeling, are well in agreement with theoretical solutions. In contrast, the results calculated for the same model, using original first‐order 3‐D DDA are far from the theoretical solutions. Copyright © 2009 John Wiley & Sons, Ltd.