A methodology for scaling non-linear force-displacement behavior of elastomeric isolators for design
Bibliographic record
Abstract
Base isolation systems may perform differently in practice than in theoretical predictions due to factors such as environmental conditions, aging, temperature fluctuations, scragging, and the natural variability of rubber materials and the manufacturing processes. These factors significantly influence the mechanical behavior of base isolators, affecting their characteristic strength, damping, and stiffness, which consequently impacts the performance of both the isolation system and the superstructure. Most standards emphasize that isolator design should not rely solely on nominal values, leading to the introduction of property modification factors, commonly referred to as λ -factors, to account for the variability in the mechanical behavior of base isolators. These factors were originally defined for bilinear or trilinear force-displacement behaviors. Their application to more complex models has been theorized without clear guidance on how they should be implemented. This study presents a method for scaling the effective stiffness, K eff , and enclosed hysteresis area, W , in the force-displacement behavior of isolators for complex numerical models such as the Bouc-Wen model, modified Bouc-Wen model, and the algebraic model, which are commonly used for modeling elastomeric isolators. Unlike characteristic strength, Q d , and post-yield stiffness, K d , which are typically employed in bilinear and trilinear models, the K eff and W were chosen because they offer a more general and practical representation of highly nonlinear devices, which often lack well-defined Q d and K d values. The proposed approach can independently scale the K eff and W within the ranges specified by AASHTO, ASCE 7–22, and ASCE 7–41. This approach can be extended to other isolator mechanical properties and numerical models. • Proposes a method for scaling effective stiffness, K eff , and hysteresis area, W , in advanced isolator models. • Extends application of the λ -factors concept beyond bi- and trilinear models to Bouc-Wen, modified Bouc-Wen, and algebraic models. • Provides a scalable framework to independently adjust K eff and W while ensuring compatibility with relevant guidelines. • Demonstrates the method's effectiveness across a wide range of λ -factors and its generalizability to numerical models.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| 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) | 0.002 | 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".