Structures under Multiple Design-Dependent Loads: Topology Optimization Enabled by Load Thresholding and Sensitivity Scaling
Bibliographic record
Abstract
Abstract Topology optimization of structures subjected to both design-independent loads, such as point forces and constant elevated temperatures, and design-dependent loads, including distributed temperature and pressure abound. However, fewer studies have addressed the optimization of structures when multiple design-dependent load cases interact. This study focuses on optimizing a rotating structure subject to an elevated temperature distribution and a point force. Firstly, we establish theoretical frameworks for thermoelastic stress loads, steady-state heat transfer, and rotational inertia loads. Secondly, we introduce the concept of load thresholding for managing complex load conditions. Thirdly, we develop a weighted multi-objective topology optimization framework and perform sensitivity analysis for a combination of design-dependent loads (centrifugal and thermoelastic stress loads) and design-independent point force. To enhance numerical stability, we incorporate scale factors into the consolidated sensitivity equation. Our results demonstrate that the adoption of load thresholding, sensitivity scaling, and reduced weight factors (typically below 0.5) for TSLs and centrifugal loads not only reduces numerical instabilities but also yields structures with lower compliance values and more distinctive topologies.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 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".