Evolutionary level set method for crashworthiness topology optimization

Vehicle crashworthiness design belongs to one of the most complex problems considered in the design optimization. Physical phenomena that are taken into account in crash simulations range from complex contact modeling to mechanical failure of materials. This results in high nonlinearity of the optimization problem and involves remarkable amount of numerical noise and discontinuities of the objective functions that are optimized. Consequently, the sensitivity information, which is necessary for the majority of Topology Optimization approaches, can be obtained analytically only for considerably simplified problems, which, in most cases, excludes the use of the gradient-based optimization methods. As a result, in the state-of-theart methods for crashworthiness Topology Optimization, strong and thus arguable assumptions about the properties of the optimization problem are made and heuristic approaches are used. This problem can be solved with use of Evolutionary Algorithms, where no assumptions about the optimization problem have to be made and which perform well even for highly nonlinear and discontinuous problems. We propose a novel approach using evolutionary optimization techniques together with a geometric Level-Set Method in crashworthiness Topology Optimization. Both standard Evolution Strategies and the state-of-the-art Covariance Matrix Adaptation Evolution Strategy are used. In order to evaluate the proposed method, an energy maximization problem for a rectangular beam, fixed at both ends and impacted in the middle by a cylindrical pole, is considered. The results show that the evolutionary optimization methods can be efficiently used for an optimization of crash-loaded structures, while defining the objective function explicitly.