Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 61, Issue 3, Pages 433-454Publisher
WILEY
DOI: 10.1002/nme.1075
Keywords
strain gradient theory; finite element method; C0-1 patch test
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Based on finite element formulations for the strain gradient theory of microstructures, a convergence criterion for the C0-1 patch test is introduced, and a new approach to devise strain gradient finite elements that can pass the C0-1 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 C0-1 patch test. The difference between the proposed C0-1 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 C0-1 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 C0-1 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 (C) 2004 John Wiley Sons, Ltd.
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