Stress-Constrained Multi-Material Topology Optimization
Bibliographic record
Abstract
The study and application of Topology Optimization (TO) has experienced great maturity in recent years, presenting itself as a highly influential and sought-after design tool in both the automotive and aerospace industries. TO has experienced development from single material topology optimization (SMTO) to multi-material topology optimization (MMTO), where material selection is simultaneously optimized with material existence. Today, MMTO for standard structural optimization responses are well supported. An additional and vital response in the design of structures is that of stress. Stress-driven or stress-controlled optimization techniques for SMTO are well understood and have been well-documented, evidenced by both published works and its availability in multiple commercial solvers. However, its integration into MMTO frameworks has not yet achieved reliable levels of accuracy and flexibility. The principal limitation of existing stress-constrained MMTO methodologies is the inability to consider candidate material-specific stress limits. Another limitation is that candidate materials cannot have different Poisson’s ratios. Herein, the study of stress-constrained MMTO is extended to consider material-specific yield stresses by introducing a novel stress limit interpolation scheme on P-norm aggregation scheme. Moreover, a stress correction method is extended from SMTO to MMTO, to avoid the stress overestimation issue. In support of the discussion on the constraint and its characteristics, its sensitivities are derived. The proposed method is examined on both 2D and 3D models, including the comparison to the results obtained by the existing commercial solver and on models with more than one million elements or multiple load cases to present the effectiveness of the proposed method.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".