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.