Crashworthiness Design using Topology Optimization

Vehicle crashworthiness design is one of the most difficult problems being addressed in design optimization. This is due to themodeling of the complex interactions involved in the crash process, such as material and geometric nonlinearities, contact between elements,strain rate effects, among other phenomena. The goal of crashworthiness design is to improve passenger safety subject to manufacturingcost constraints. Many current approaches utilize a parameterized optimization approach that requires response surface approximations of the design space. This is due to the expensive nature of numerical crash simulations and the high nonlinearity and noisiness in the design space due to the aforementioned phenomena. Thesemethodologies usually require a significant design effort to determine an initial design. This is where topology optimization is of great benefit.The primary goal of this dissertation is the development of a topology optimization approach for application to vehicle crashworthiness design that utilizes high fidelity crash simulations. Topology optimization is an iterative process that determines the best arrangement of material so as to obtain an optimal performance of the concept design. These design problems involve thousands of variables and thus can lead to large computational efforts for gradient-based optimizers. The complexities in deriving analytical sensitivities for a dynamic analysis and expensive computational time associated with numerical calculation of the sensitivities for this analysis have hindered research in crashworthiness design optimization. The methodology developed in this research is a non-gradient approach that utilizes the cellular automata paradigm and follows the principles of fully stressed design to generate the concept designs.The secondary goal of the research is the development of constraints on cost and performance. Cost is considered through constraints on available material and constraint on material distribution so that the final topology is amenable to the simple extrusion manufacturing process. The methodologies developed in this research are applied to practical design problems. The results demonstrate that the inclusion of multiple load cases requires some careful consideration. The results demonstrate that the methodologies provide a practical technique and tool to aid the design engineer in the generation of design concept of crashworthy structures.