Multi-material topology optimization considering natural frequency constraint
Why this work is in the frame
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Bibliographic record
Abstract
Purpose The purpose of this paper is to propose an effective and efficient numerical method that can consider natural frequency in multi-material topology optimization (MMTO) and which is scalable for complex three-dimensional (3D) problems. Design/methodology/approach The optimization algorithm is developed by combining custom FORTRAN code for MMTO with the open-source software Mystran, which is used as a finite element analysis (FEA) solver. The proposed algorithm allows the designer to shift the fundamental frequency of the design beyond a defined frequency spectrum from the initial designing phase. The methodology is formulated in a smooth and differentiable manner, with the sensitivity expressions, required by gradient-based optimization solvers, presented. Findings Natural frequency constraint has been successfully implemented into MMTO. The use of open-source software Mystran as an FEA solver in the algorithm provides ability to solve complex problems. Mystran offers powerful built-in functions for eigenvalue extraction using methods like Givens, modified Givens, inverse power and the Lanczos method, which provide the ability to solve complex models. The algorithm is successfully able to solve both two- and three-material MMTO jobs for two-dimensional and 3D geometries. Originality/value Natural frequency constraint consideration into topology optimization is very challenging due to three common issues: localized eigenmodes, mode switching and high computational cost. The proposed algorithm addresses these inherent issues, implements natural frequency constraint to MMTO and solves for complex models, which is hardly possible using conventional methods.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it