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DESIGN OF MULTI-MATERIAL STRUCTURES FOR CRASHWORTHINESS USING HYBRID CELLULAR AUTOMATON
The design of vehicle components for crashworthiness is one of the most challenging problems in the automotive industry. The safety of the occupants during a crash event relies on the energy absorption capability of vehicle structures. Therefore, the body components of a vehicle are required to be lightweight and highly integrated structures. Moreover, reducing vehicle weight is another crucial design requirement since fuel economy is directly related to the mass of a vehicle. In order to address these requirements, various design concepts for vehicle bodies have been proposed using high-strength steel and different aluminum alloys. However, the price factor has always been an obstacle to completely replace regular body steels with more advanced alloys. To this end, the integration of numerical simulation and structural optimization techniques has been widely practiced addressing these requirements. Advancements in nonlinear structural design have shown the promising potential to generate innovative, safe, and lightweight vehicle structures. In addition, the implementation of structural optimization techniques has the capability to shorten the design cycle time for new models. A reduced design cycle time can provide the automakers with an opportunity to stay ahead of their competitors. During the last few decades, enormous structural optimization methods were proposed. A vast majority of these methods use mathematical programming for optimization, a method that relies on availability sensitivity analysis of objective functions. Thus, due to the necessity of sensitivity analyses, these methods remain limited to linear (or partially nonlinear) material models under static loading conditions. In other words, these methods are no able to capture all non-linearities involved in multi-body crash simulation. As an alternative solution, heuristic approaches, which do need sensitivity analyses, have been developed to address structural optimization problems for crashworthiness. The Hybrid Cellular Automaton (HCA), as a bio-inspired algorithm, is a well-practiced heuristic method that has shown promising capabilities in the structural design for vehicle components. The HCA has been continuously developed during the last two decades and designated to solve specific structural design applications. Despite all advancements, some fundamental aspects of the algorithm are still not adequately addressed in the literature. For instance, the HCA numerically implemented as a closed-loop control system. The local controllers, which dictate the design variable updates, need parameter tuning to efficiently solve different sets of problems. Previous studies suggest that one can identify some default values for the controllers. However, still, there is no well-organized strategy to tune these parameters, and proper tuning still relies on the designer’s experience.
Moreover, structures with multiple materials have now become one of the perceived necessities for the automotive industry to address vehicle design requirements such as weight, safety, and cost. However, structural design methods for crashworthiness, including the HCA, are mainly applied to binary structural design problems. Furthermore, the conventional methods for the design of multi-material structures do not fully utilize the capabilities of premium materials. In other words, the development of a well-established method for the design of multi-material structures and capable of considering the cost of the materials, bonding between different materials (especially categorical materials), and manufacturing considering is still an open problem. Lastly, the HCA algorithm relies only on one hyper-parameter, the mass fraction, to synthesize structures. For a given problem, the HCA only provides one design option directed by the mass constraint. In other words, the HCA cannot tailor the dynamic response of the structure, namely, intrusion and deceleration profiles.
The main objective of this dissertation is to develop new methodologies to design structures for crashworthiness applications. These methods are built upon the HCA algorithm. The first contribution is about introducing s self-tuning scheme for the controller of the algorithm. The proposed strategy eliminates the need to manually tune the controller for different problems and improve the computational performance and numerical stability. The second contribution of this dissertation is to develop a systematic approach to design multi-material crashworthy structures. To this end, the HCA algorithm is integrated with an ordered multi-material SIMP (Solid Isotropic Material with Penalization) interpolation. The proposed multi-material HCA (MMHCA) framework is a computationally efficient method since no additional design variables are introduced. The MMHCA can synthesize multi-material structures subjected to volume fraction constraints. In addition, an elemental bonding method is introduced to simulate the laser welding applied to multi-material structures. The effect of the bonding strength on the final topology designs is studied using numerical simulations. In the last step, after obtaining the multi-material designs, the HCA is implemented to remove the desired number of bonding elements and reduce the weld length.
The third contribution of this dissertation is to introduce a new Cluster-based Structural Optimization method (CBSO) for the design of multi-material structures. This contribution introduces a new Cluster Validity Index with manufacturing considerations referred to as CVIm. The proposed index can characterize the quality of the cluster in structural design considering volume fraction, size, interface as a measure of manufacturability. This multi-material structural design approach comprises three main steps: generating the conceptual design using adaptive HCA algorithm, clustering of the design domain using Multi-objective Genetic Algorithm (MOGA) optimization. In the third step, MOGA optimization is used to choose categorical materials in order to optimize the crash indicators (e.g., peak intrusion, peak contact force, load uniformity) or the cost of the raw materials. The effectiveness of the algorithm is investigated using numerical examples.