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Finite element formulations of strain gradient theory for microstructures and the C 0–1 patch test
Author(s) -
Soh AiKah,
Wanji Chen
Publication year - 2004
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.1075
Subject(s) - finite element method , spurious relationship , mathematical analysis , mathematics , geometry , displacement (psychology) , convergence (economics) , eigenvalues and eigenvectors , zero (linguistics) , strain (injury) , constant (computer programming) , physics , structural engineering , engineering , computer science , psychology , statistics , quantum mechanics , economics , psychotherapist , economic growth , medicine , linguistics , philosophy , programming language
Based on finite element formulations for the strain gradient theory of microstructures, a convergence criterion for the C 0–1 patch test is introduced, and a new approach to devise strain gradient finite elements that can pass the C 0–1 patch test is proposed. The displacement functions of several plane triangular elements, which satisfy the C 0 continuity and weak C 1 continuity conditions are evaluated by the C 0–1 patch test. The difference between the proposed C 0–1 patch test and the C 0 constant stress and C 1 constant curvature patch tests is elucidated. An 18‐DOF plane strain gradient triangular element (RCT9+RT9), which passes the C 0–1 patch test and has no spurious zero energy modes, is proposed. Numerical examples are employed to examine the performance of the proposed element by carrying out the C 0–1 patch test and eigenvalue test. The proposed element is found to be without spurious zero energy modes, and it possesses higher accuracy compared with other strain gradient elements. Copyright © 2004 John Wiley & Sons, Ltd.