Crashworthiness design is an evolving discipline that combines vehicle crash simulation and design synthesis. The goal is to increase passenger safety subject to manufacturing cost constraints. The crashworthiness design process requires modeling of the complex interactions involved in a crash event. Current approaches utilize a parametrized 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. These methodologies usually require a significant effort to determine an initial design concept. In this paper, a heuristic approach to continuum-based topology optimization is developed for crashworthiness design. The methodology utilizes the cellular automata paradigm to generate three-dimensional design concepts. Furthermore, a constraint on maximum displacement is implemented to maintain a desired performance of the structures synthesized. Example design problems are used to demonstrate that the proposed methodology converges to a final topology in an efficient manner.