Efficient finite element response sensitivity analysis and applications in composites manufacturing
Bibliographic record
Abstract
This thesis presents the development, implementation, and application of response sensitivities in numerical simulation of composite manufacturing. The sensitivity results include both first- and second-order derivatives. Such results are useful in many applications. In this thesis, they are applied in reliability analysis, optimization analysis, model validation, model calibration, as well as stand-alone measures of parameter importance to gain physical insight into the curing and stress development process. In addition to novel derivations and implementations, this thesis is intended to facilitate and foster increased use of response sensitivities in engineering analysis. The work presented in this thesis constitutes an extension of the direct differentiation method (DDM). This is a method that produces response sensitivities in an efficient and accurate manner, at the one-time cost of deriving and implementing sensitivity equations alongside the ordinary response algorithm. In this thesis, novel extensions of the methodology are presented for the composite manufacturing problem. The derivations include all material, geometry, and processing parameters in both the thermochemical and the stress development algorithms. A state-of-the-art simulation software is developed to perform first-order sensitivity analysis for composite manufacturing problems using the DDM. In this software, several novel techniques are employed to minimize the computational cost associated with the response sensitivity computations. This sensitivity-enabled software is also used in reliability, optimization, and model calibration applications. All these applications are facilitated by the availability of efficient and accurate response sensitivities. The derivation and implementation of second-order sensitivity equations is a particular novelty in this thesis. It is demonstrated that it is computationally feasible to obtain second-order sensitivities (the “Hessian matrix”) by the DDM for inelastic finite element problems. It is demonstrated that the direct differentiation approach to the computation of first- and second-order response sensitivities becomes increasingly efficient as the problem size increases, compared with the less accurate and less efficient finite different approach.
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How this classification was reachedexpand
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) | 0.000 | 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 teacher head, 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".