Multi-Material Topology Optimization Considering Crashworthiness
Bibliographic record
Abstract
There is an increasing need for lightweight structures in the transportation industry, and within these lightweight structures occupant safety is continually important to all stakeholders. Standard single and multi-material topology optimization (MMTO) techniques are effective for designing lightweight structures subjected to linear objectives and constraints but cannot consider crashworthiness. Crashworthiness must be evaluated using explicit dynamic simulation techniques, as a crash event contains geometric and material nonlinearities which cannot be captured by linear static finite element simulations. Explicit dynamic simulations prevent the calculation of sensitivity derivatives required for conventional gradient-based structural optimization strategies. This paper describes a design tool for multi-material topology optimization considering crashworthiness using the equivalent static load (ESL) method. The ESL method is used to generate linear static sub-problems which replicate the dynamic structural response of explicit dynamic crash simulations in the linear regime. The ESL sub-problems are input to a standard MMTO, optimized results from which are used as input for subsequent crash analyses to update the ESLs for additional sub-problems. The ESLs evolve as the design changes – convergence occurs when the design does not change significantly between subsequent sub-problem optimizations. The objective of this paper is to demonstrate a methodology for an efficient design tool for MMTO considering crashworthiness. Firstly, the ESL and competing methods for crashworthiness optimization are introduced and compared. Next a discussion of the tool’s operation flow as well as the sensitivity equations are presented along with two academic examples demonstrating its implementation. The design tool generates optimized multi-material designs which outperform single-material optimized designs in terms of mass by 7.5% and 17.6% in 2D and 3D models respectively when subjected to crash load cases.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".