Multi-Joint Topology Optimization: A Method for Considering Joining in Multi-Material Design
Bibliographic record
Abstract
Automakers are under constant pressure to improve fuel economy and vehicle range to achieve a competitive advantage within the industry and meet government regulations. Reducing the overall weight of a vehicle contributes significantly to achieving this goal. Topology optimization (TO) has been identified within industry as a leading method to reduce weight on both a component and assembly level. With this tool, components can be redesigned to maintain structural performance requirements while also providing significant weight savings. On an assembly level, TO can be used to determine optimal loadpaths within large structures such as frames or bodies. These loadpaths can be interpreted to determine the locations of different components within the structure. To support the development of lightweight vehicle design, this paper presents a revised methodology and application of multi-joint topology optimization (MJTO). This method is an extension of multi-material topology optimization (MMTO), which is derived from the classical standard single-material problem statement (SMTO). Here, MJTO both extends topology optimization to consider multiple materials while also considering joint characteristics between material boundaries. Included here is a detailed description and demonstration of the MJTO methodology, starting with a brief overview of MMTO. Next, the derivation of MJTO element interpolation functions, sensitivities, and filtering methods are presented with the introduction of a novel mesh independent gradient approximation method. This method extends MJTO to problems with irregular mesh types and addresses issues with previously adopted approaches. Finally, a case study is presented demonstrating the MJTO method and providing a holistic comparison between SMTO and MMTO solutions.
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".