A Newmark Integral Method in Nonhomogeneous Materials With Parallel Cracks Based on Hyperbolic Heat Conduction
Bibliographic record
Abstract
The strong, transient working conditions where heat transfer involves extremely large temperature gradients, extremely large heat fluxes, and extremely short time durations of thermal disturbances may occur in engineering materials and structures. Fourier heat conduction assumes heat propagation at an infinite speed, which is not suitable for strong, transient thermal working conditions. In this paper, a Newmark integral method is presented to deal with the strong, transient heat conduction in nonhomogeneous materials based on the hyperbolic heat conduction theory. The second‐order differential equation of the strong transient temperature field is discretized in the spatial and temporal domains through the finite element method (FEM) and the Newmark integral method, respectively. This allows them to be solved directly without the necessity to convert them into a pair of first‐order differential equations using the Newmark integral method. Several test examples are presented to demonstrate the application of the current method. Firstly, the stability of the Newmark integral method is analyzed to ensure that the numerical oscillation is suppressed in the calculation. Then the time‐related temperature field of functionally graded material (FGM) plate under strong transient thermal shock is analyzed. Finally, the thermal stress intensity factors (TSIFs) in an FGM plate with parallel cracks are extracted after combining with interaction energy integral methods (IEIMs). The results confirm that the Newmark integral method can efficiently address the transient thermal problem and ensure stability. The temperature overshooting phenomenon and thermal wave singularity are visualized at the finite speed of heat propagation. Moreover, the numerical results agree well with analytical solutions. The current method can be well applied to the design and evaluation of thermal protective materials in extreme thermal environments.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".