A new five‐node locking‐free quadrilateral element based on smoothed FEM for near‐incompressible linear elasticity
Bibliographic record
Abstract
SUMMARY The volumetric locking issue is critical in finite element analysis of nearly incompressible problems. In this paper, a new five‐node quadrilateral element (Q5) is proposed by enriching the four‐node quadrilateral element (Q4) with a centroid node to solve the volumetric locking problem in FEM. The cell‐based smoothed FEM is employed with Q5 element (referred as Q5‐CS‐SC4) to soften the stiffness in order to obtain a better solution. To eliminate pressure oscillation in near‐incompressible problems, an edge‐based area‐weighted smoothing scheme incorporated with the cell‐wise divergence‐free Q5 element is carried out (referred as Q5‐EAW), and an adjustable area‐weighted strain smoothing scheme using a parameter p is proposed to improve the performance of the Q5 element in dealing with incompressible media (referred as Q5‐pEAW). The formulation of Q5‐pEAW is a simple combination of Q5‐CS‐SC4 and Q5‐EAW by an adjustable area weight. It can search the exact strain energy of the problem in near‐incompressible cases. We also introduce another node‐based strain smoothing technique (Q5‐NAW) into the domain‐based selective scheme to obtain a Q5‐pEAW/NAW model to solve the pressure oscillation, which gives a much smoother pressure solution than Q5‐EAW. Finally, the Q5 element is extended into hexahedral element to develop a nine‐node hexahedral (H9) element shape function by enriching the eight‐node hexahedral element (Q8) with a centroid node. An H9‐Gi/NAW model similar to Q5‐pEAW/NAW is proposed by using H9 element to solve the 3D volumetric locking. A series of benchmark problems are provided to demonstrate that the proposed Q5‐pEAW/NAW for 2D plane strain problems, and H9‐Gi/NAW model for 3D cases are locking‐free for nearly incompressible problems. Copyright © 2014 John Wiley & Sons, Ltd.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".