STOCHASTIC DESIGN OPTIMIZATION FOR VIBRATION AND IMPACT MITIGATION

Abstract

The reliability assessment and computational design of nonlinear dynamic problems require new optimization and uncertainty quantification approaches that are tailored to address the associated challenges. Namely, these problems are computationally expensive and highly sensitive to uncertainties since they model nonlinear dynamic phenomena. This work focuses on uncertainty quantification and design optimization of nonlinear dynamic problems for vibration and impact mitigation by applying state-of-the-art probabilistic methods. While such problems cover a wide range of applications, this work highlights two main applications and develops novel approaches to tackle the existing computational challenges. The first application is the stochastic optimization of nonlinear metamaterials for the manipulation and mitigation of waves. A nonlinear chain of resonators representing metamaterials is considered, in which response discontinuity and curse of dimensionality, in addition to the challenges mentioned above, hamper the traditional engineering design methods. For this purpose, the methodology that is applied tackles a discontinuous response by identifying the regions of space with vastly different response levels. Additionally, to reduce the dimensionality of the problem, a field formulation is proposed that defines numerous properties of the resonators (e.g., stiffnesses) through a handful of coefficients. The uncertainties are also taken into account by considering random design variables and loading conditions. It is illustrated that the resonators chain optimized using the algorithm is able to reliably and effectively suppress vibrations. The second application deals with vehicle crashworthiness optimization and injury risk assessment under uncertainty for improving safety. The crashworthiness problem involves the finite element simulations of a sled model and an occupant restraint system, whose responses are non-smooth due to simulation noise. In this regard, an optimization algorithm is developed based on the Non-Deterministic Kriging (NDK) formulation, which is used to approximate the response while accounting for the simulation noise and random parameters (e.g., loading conditions) as aleatory sources of uncertainties. To reduce the dimensionality of optimization problems, this algorithm accounts for random uncontrollable parameters through the aleatory covariance of the NDK kriging. An improvement of an existing adaptive sampling method is also proposed to enhance the performance of the optimization algorithm. The advantages of the methodology are illustrated using multiple analytical functions and the crashworthiness problem. In addition to the optimization algorithm, an injury risk model is developed to calculate the probability of crash-induced head injuries through the fusion of two information sources: a published experiment-based risk model and a finite element framework. The framework involves the finite element model of a car, a human dummy, and a human brain. It integrates sources of uncertainty such as impact conditions (e.g., velocity and angle) and brain material properties.