Frequency-Constrained Multi-Material Topology Optimization: Commercial Solver Integrable Sensitivities
Bibliographic record
Abstract
Numerical tools such as topology optimization (TO) have seen large development in both academic and industrial settings, enabling the optimization of structural objectives and/or attributes, subject to a wide range of constraints, pertinent to the engineering and design problems of automotive and aerospace industries. Classical TO methods assume the use of a single material (SMTO), however, a recent and important advancement in this field is that of multi-material topology optimization (MMTO), capable of simultaneous material existence and selection optimization. This is of heightened importance in the aforementioned industries, where many costly engineering materials can be used, but their selection is delegated to engineer experience. Consideration of modal characteristics (i.e., natural frequencies) in MMTO efforts have seen marginal development in recent years, yet is vital to both industries, who’s products are each subject to uncontrolled environments and vibratory motion. Where frequency has been considered in MMTO, mathematical frameworks require the usage of model attributes that are not extractable from commercial finite element analysis (FEA) solvers, leading to reduced computational efficiency. This paper presents an advancement of the frequency-constrained MMTO sensitivities previously utilized in SMTO, enabling the use of commercial solvers, thus inheriting computational improvements. A derivation of sensitivities, a detailed discussion, and analysis of two case studies have been included, so as to provide the reader with a sound understanding of the nature of the constraint sensitivities, and how they may be able to intuit results.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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 | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.010 | 0.002 |
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".