Crashworthiness design of cross-sections with the Graph and Heuristic based Topology Optimization incorporating competing designs

This contribution presents a method for finding cross-section designs of crashworthiness profiles. The method combines mathematical optimization algorithms with heuristics that are based on expert knowledge. A novel version of the Graph and Heuristic based Topology Optimization (GHT) with a scheme, which pursues different competing designs, will be presented. This sequence reduces the number of necessary crash simulations and improves the ability of the method to overcome local optima. The occurring nonlinearities of crashworthiness problems present major challenges in the optimization process: geometry (e.g., large displacements and rotations), boundary condition (e.g., contact), and material (e.g., plasticity, failure, and strain rate dependency). Furthermore, the large number of design variables, the existence of bifurcation points, and the expensive determination of gradient information pose additional challenges. In the GHT, the actual optimization problem is divided into two optimization loops nested in each other. In the outer optimization loop, heuristics derived from expert knowledge change the topology of the structure based on simulation data from crash simulations. In the inner optimization loop, conventional universal optimization algorithms are used for shape and sizing optimizations to evaluate and improve the suggested designs. The geometry of the profile cross-section is described by a mathematical graph. The graph is generated according to a syntax that allows complex geometric modifications such as topology changes. Graph-based algorithms are used for checking the geometry to ensure the manufacturability of the designs at any time of the optimization process.