An effective topology optimization method for crashworthiness of thin-walled structures using the equivalent linear static loads

Abstract

The equivalent static loads method for nonlinear dynamic response structural optimization may be failed in large deformation crash conditions, due to topology optimization with the equivalent static loads mostly beyond the linear range and causing numerical defects such as high compliance of elements. To overcome the above disadvantage, an advanced structural topology optimization method for crashworthiness considering crash-reduced large deformation and plastic buckling is proposed using newly defined equivalent linear static loads. The equivalent linear static loads can adaptively scale to guarantee that the topology optimization is performed within linear range. At each cycle, the crash simulation is performed and the nonlinear nodal displacement vector at the time step with the maximum strain energy is scaled by an adaptive displacement-scaling factor. The equivalent linear static loads that are generated by multiplying the linear stiffness matrix and the scaled nodal displacement vector will be incorporated into topology optimization, which can guarantee the topology optimization to remain in linear range and further solve the numerical instability problems. The process is repeated until the convergence criteria are satisfied. The effectiveness of the proposed method is evaluated by solving a crashworthiness topology optimization of a crash box considering crash-induced plastic buckling to determine the location and profile of crash triggers. The results show that the proposed method can effectively solve the large deformation crashworthiness topology optimization of thin-walled structures and provides a feasible strategy for crash triggers design in crash box.

Electric vehicles body frame structure design method: An approach to design electric vehicle body structure based on battery arrangement

“…Collision simulation of designed schemes can be used to compare the energy absorption capability of the body frame. 5,47 For the impact analysis, the peak acceleration can be used to evaluate the energy absorption characteristics of the body structure. 52,53 The intersection of B-pillar and threshold beam as acceleration measurement point, 13 the maximum collision acceleration at the measurement point is 56.09 g in Scheme I and 62.54 g in Scheme II, as shown in Table 10.…”

“…Six typical load cases for topology optimization are selected, including three static load cases and three dynamic impact loading scenarios, based on EV’s regulations and research results. 12,13,47 The static load cases are torsion and bending which contains two concentrated loads and one uniform load according to battery weight 12 to ensure the stiffness and stability of body structure. The dynamic load cases are specified by C-NCAP 38 for energy vehicles, which are 100% overlapping rigid wall collision condition, frontal 50% overlapping deformable barrier collision and side column collision.…”

“…The cross section of profiles is designed the same as Section 4.1 using topology optimization under multiple load cases to obtain load paths. 27,47 The weight of each load case is determined by the load-bearing and energy-absorbing capacity the component. Taking crash box as an example, the main function of the crash box is crush deformation and energy absorption in frontal collision.…”

Plate manufacturing constraint in topology optimization using anisotropic Helmholtz filter

“…In recent years, topology optimization has been applied to many other performance areas in addition to linear stiffness, such as elastoplastic (Yuge and Kikuchi, 1995;Forsberg and Nilsson, 2007;Ren et al, 2020), viscoelastic (Park et al, 2021), and vibration (Ma et al, 1993(Ma et al, , 1995 analyses. Buckling (Neves et al, 1995;Kamada et al, 2021) is also a concern, especially when dealing with sheet metal, but it is not always possible to obtain appropriate stress directions in a nonstatic analysis.…”