Non-linear dynamic response structural optimization of an automobile frontal structure using equivalent static loads

Abstract

Although the capability of the computer has been developed and numerical algorithms have been advanced, automobile crash optimization is still quite difficult owing to high non-linearity and numerical cost. Therefore, metamodel-based optimization methods have been frequently utilized in crashworthiness optimization. However, the methods have various limits on the number of design variables and precision. The equivalent-static-loads (ESLs) method has been proposed to overcome the limitations. ESLs are static loads which generate the same displacement field in static analysis as the displacement field at each time step in non-linear dynamic analysis; they are used as the external loads for linear static response optimization. The results of linear static response optimization are utilized to update the design, and non-linear dynamic analysis is performed again with the updated design. The process proceeds in an iterative manner until the convergence criteria are satisfied. From various research studies on the ESLs method, it has been demonstrated that the ESLs method is fairly useful. An automobile frontal structure is optimized for the pendulum test. The optimization problem is formulated with many design variables including displacement, velocity, and acceleration constraints. A method is proposed for handling the velocity and acceleration constraints by using the finite difference method. In a numerical analysis of the pendulum test, the velocity and acceleration are extremely non-linear and noisy. Thus, a filtering technique is utilized for the displacement, velocity, and acceleration curves. LS-DYNA is used for non-linear dynamic analysis, and NASTRAN is used for linear static response optimization and generation of ESLs. The SAE 60 filter in LS-PRE/POST is used to filter the displacement response. A program is developed for interfacing the two systems.

Vehicle crash optimization considering a roof crush test and a side impact test

“…Many studies using ESLM have been reported with regard to practical crash optimization problems. 4,15,16,19,20,30…”

“…Therefore, crash analysis and linear static response structural optimization are cyclically repeated until the convergence criterion is satisfied. In general, ESLM can find an optimum solution with a small number of crash analyses 16–20 and can consider size, shape, and topology optimizations in a unified manner. 21–23 Lee and Park 4 solved crash optimization with regard to the IIHS side impact test.…”

Non-linear dynamic response structural optimization for frontal-impact and side-impact crash tests

“…2, 6–8, 10–12, 32–39 In the late 1990s, Choi et al 12 introduced the ESLM for linear dynamic response optimization, and the method has been expanded to various disciplines such as flexible multi-body dynamic systems, 34, 40–42 rigid-body dynamic systems, 43 non-linear static systems, 10, 36, 37 and non-linear dynamic systems. 5–8, 11, 32, 33, 35, 39, 44, 45 Jeong et al 6 compared the ESLM and the response surface method with regard to the roof structure of a vehicle. Kim and Park 8 compared the ESLM and the conventional method subject to stress constraints.…”

“…4 The ELSM was proposed to overcome these problems, and it has been applied to large and practical examples. 5–11 This method has an analysis domain and a design domain. 12 Non-linear dynamic analysis is performed in the analysis domain, equivalent static loads (ESLs) are generated and gradient-based linear static structural optimization is carried out with the ESLs in the design domain.…”

Nonlinear dynamic response structural optimization using equivalent static loads

“…Two more practical examples are also introduced to show the possibility of applying the method to real engineering problems. They are nonlinear dynamic response structural optimization of a joined-wing [26] and an automobile frontal structure [27]. They have a large scale finite element model and need a long CPU time with many design variables and constraints.…”