title: Crashworthiness Optimization using difference-based equivalent static Loads - Sizing and Topology Optimization of Structures subjected to Crash
Creators: name: Triller, Jens
Publisher: name: UNSPECIFIED
Year: 2023

description: Structural optimization of crash related problems usually involves nonlinearities in geometry, material, and contact. For such kinds of problems, the sensitivities are either not available or very expensive to compute. Efficient gradient-based optimizers can then not be employed directly. The Difference-based Equivalent Static Load (DiESL) method provides a procedure to circumvent the sensitivity calculation of the original nonlinear dynamic problem by creating linear auxiliary load cases enabling gradient-based optimization. Each linear auxiliary load case then represents one specific time step of the original nonlinear dynamic problem. In this thesis various extensions of the DiESL method are presented and the method is compared to several other relevant approaches in this field. It is demonstrated how an appropriate selection of the time steps in each cycle can improve the DiESL method's approximation quality. For this purpose, the time steps are selected adaptively such that an appropriate curve, indicating the structure's nonlinear behavior, is fitted by the selected time steps. It turns out that this leads to better optimization results and more reliable convergence behavior. The DiESL method also enables the adaption of path-dependent structural properties of the original nonlinear dynamic problem like material stiffness in each linear auxiliary load case. In this thesis, an adaption of the Young’s modulus and Poisson's ratio on element level in the linear auxiliary load cases corresponding to the local plasticization in the nonlinear dynamic problem is tested. Therefore, a bilinear material model is employed in the auxiliary load cases. Here, the test examples indicate that an observable improvement can only be obtained if the material of the nonlinear dynamic problem is also idealized bilinearily and the portion of elements in the elastic and the plastic range is balanced such that the structure’s behavior is not dominated by one of both. Crashworthiness design usually involves two contradictory objectives: the structure's stiffness as well as its energy absorption behavior. To be able to address the latter, an approach for handling crash forces with the DiESL method is developed and tested using sizing optimization examples. The respective results are validated by comparing them to the theoretically known optimum or other state of the art methods. Moreover, the DiESL method is extended to topology optimization utilizing the Solid Isotropic Material with Penalization approach (SIMP). The method is tested using three examples. The first is a rigid pole colliding with a simple beam structure, where the intrusion of the pole is minimized. The initial velocity of the pole is varied in order to examine the influence of inertia effects on the optimized structures. It is shown that the results differ significantly depending on the chosen initial velocity and, consequently, that they exhibit inertia effects. Moreover, considerable improvement in terms of the resulting objective function's value could be achieved employing the DiESL method when compared with the standard ESL method for high initial velocities. The second example is an extruded rocker colliding with a rigid pole, where also the intrusion of the pole is minimized. The DiESL method yields equally good results as the Graph and Heuristic Topology optimization (GHT) approach does. However, the number of nonlinear analyses necessary to achieve convergence is significantly smaller when using the DiESL method. Finally, a rail reinforced by an additive manufactured rib is optimized. Here, several optimization runs are executed. The reaction force is maximized, while the mass of the rib is constrained to various fractions of the original rib's mass. This formulation aims to find designs where the original rib's mass and thus the related production cycle time is reduced, while its stiffness is almost maintained. In doing so a mass reduction of 30% could be achieved.