Abstract:
This paper presents a methodology for evaluating the stochastic behavior of highly non-linear structures, where variations in structural responses can stem from both deterministic parameter changes and process-induced instabilities. Utilizing response surface methodology, the authors distinguish between predictable variations and residual effects caused by bifurcations or physical instabilities, central to shape optimization and parametric modeling. Through analytical models, a headform impact scenario, and an occupant safety study, the work demonstrates how parametric modeling enables detailed analysis of response sensitivities and how shape optimization strategies must account for bifurcation-induced variabilities. Instability visualization tools and probabilistic evaluations, including Monte Carlo simulations enhanced by metamodels, are leveraged to quantify and understand structural uncertainties, ensuring robust design despite highly non-linear and unstable behaviors.
