Multi-Material and Multi-Objective Topology Optimization Considering Crashworthiness
Bibliographic record
Abstract
Recently, topology optimization (TO) has seen increased usage in the automotive industry as a numerical tool, greatly enhancing the accessibility and production-readiness of optimal, lightweight solutions. By natural extension of classic single material TO (SMTO), a wealth of research has been completed in multi-material TO (MMTO), enabling simultaneous determination of material selection and existence. MMTO is effective for linear static analyses, making use of structural responses that are continuously differentiable, giving itself to efficient gradient-based optimization engines. A structural response that is inherently nonlinear and transient, thus providing difficulty to the mainstay MMTO process, is that of crashworthiness. This paper presents a multi-objective MMTO framework considering crashworthiness using the equivalent static load (ESL) method. The ESL method uses a series of linear static sub-models to approximate the transient crashworthiness model. Then, the sub-models can be optimized sequentially, using a conventional MMTO program. The limitations of the existing framework are: (1) its sole focus on intrusion minimization using displacement constraints, (2) some results have checkerboard patterns despite the use of a filter. In this paper, an improved framework aims to support the weighted sum of multiple objectives such as compliance and aggregated stress, which would affect multiple performance metrics, such as intrusion, deceleration, and energy absorption. Also, the ESL load generation method is updated to reduce checkerboarding. Firstly, the MMTO theory and ESL method are introduced. Second, the operational flow of the framework is discussed. Finally, the multi-objective solutions of an example academic model are compared using Pareto Frontiers. The optimized results show 6.4% reduction of maximum intrusion and 1.5% reduction of maximum deceleration.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 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) | 0.003 | 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".