Finite element formulations of strain gradient theory for microstructures and the C0–1 patch test

✍ Scribed by Ai-Kah Soh; Chen Wanji

• Publisher: John Wiley and Sons
• Year: 2004
• Tongue: English
• Weight: 186 KB
• Volume: 61
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1075

✦ Synopsis

Abstract

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.