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Response Surface Models are often used as a surrogate for expensive black-box functions during optimization to reduce computational cost. Often, the CAE analysis models are highly nonlinear and multi-modal. A response surface approximation of such analysis as a result is highly multi-modal; i.e. it contains multiple local optima. A gradient-based optimizer working with such a response surface will often converge to the nearest local optimum. There does not exist any method to guarantee a global optima for non-convex multi-modal functions. For such problems, we propose an efficient algorithm to find as many distinct local optima as possible. The proposed method is specifically designed to work in large dimensions (about 100 ∼ 1000 design variables and similar number of constraints) and can identify most of the locally optimal solutions in a reasonable amount of time.

This paper introduces a design methodology to tailor the acceleration and displacement responses of a vehicle structure subjected to a dynamic crushing load. The proposed approach is an extension of the hybrid cellular automaton (HCA) method, through which the internal energy density is uniformly distributed within the structure. The proposed approach, referred here to as an extended HCA (xHCA) method, receives the suitable combinations of volume fraction and a finite element meta-parameter for which the algorithm synthesizes the load paths that allow the desired crash response. Lower meta-parameter values lead designs obtained by traditional optimizers, while larger values lead to designs obtained by the HCA method. Simultaneous implementation of multiple values of meta-parameters is presented here as a further development of xHCA method.

A new solution methodology for optimal spot-weld pattern design is presented. The objective of the optimization is to minimize the total number of welds in a structure while maintaining structural properties above a required level. Two approaches were developed, based on the representation of welds in a finite element model. In the approach ‘without ranking’ welds are represented in a traditional way, as rigid connections. In ‘with ranking’ approach welds are treated as elastic elements subjected to stresses and deformations under given loading conditions. The information on weld stress is utilized in the solution process to reduce the number of design variables and improve the quality of the solution. The applicability of the method to large automotive structures was demonstrated, as well as the capacity for optimization with respect to multiple load sets.

The Hybrid Cellular Automaton (HCA) algorithm is a generative design approach used to synthesize conceptual designs of crashworthy vehicle structures with a target mass. Given the target mass, the HCA algorithm generates a structure with a specific acceleration-displacement profile. The extended HCA (xHCA) algorithm is a generalization of the HCA algorithm that allows to tailor the crash response of the vehicle structure. Given a target mass, the xHCA algorithm has the ability to generate structures with different acceleration-displacement profiles and target a desired crash response. In order to accomplish this task, the xHCA algorithm includes two main components: a set of meta-parameters (in addition target mass) and surrogate model technique that finds the optimal meta-parameter values. This work demonstrates the capabilities of the xHCA algorithm tailoring acceleration and intrusion through the use of one meta-parameter (design time) and the use of Kriging-assisted optimization.

Structures with multiple materials have now become one of the perceived necessities for automotive industry to address vehicle design requirements such as light-weight, safety, and cost. The objective of this study is to develop a design methodology for multi-material structures accountable for vehicle crash durability. The heuristic topology synthesis approach of Hybrid Cellular Automaton (HCA) framework is implemented to generate multi-material structures with the constraint on the volume fraction of the final design. The HCA framework is integrated with ordered-SIMP (solid isotropic material with penalization) interpolation, artificial material library, as well as statistical analysis of material distribution data to ensure a smooth transition between multiple practical materials during the topology synthesis.