Stuctural members if a vehicle are designed to increase the energy absorption efficiency and thus to enhance the safety and reliability of a vehicle. The crashworthiness of each member needs to be evaluated at the initial state of vehicle design for good performance of an assembled vehicle. The crashworthiness simulation is usually carried out with the elastic-plastic finite element analysis code such as PAMCRASH or LS-DYNA3D. For explicit schemes, the time steps size is generally restricted by the stability criterion. It inevitably requires tremendous time and efforts to estimate the crashworthiness of structural members. An efficient, alternative analysis tool could be an extended limit method for fast evaluation of the crashworthiness of strucutural members.
Limit analysis has become a useful and efficient numerical tool in the collapse behavior assessment for structural members since the method can easily calculate the plastic collapse load, energy absorption and deformation mode. The algorithm with a simple formulation has the advantage of stable convergence, computational efficiency and easy access ti work-hardening materials. Dynamic limit analysis can evaluate the crashworthiness of structural members efficiently, accurately and systematically. Dynamic limit analysis uses the WBZ-α method which is a class of implicit scheme. For unconditionally stable implicit scheme, the step size is governed entirely by accuracy of solution and computational efficiency. For higher accuracy, decrease of time step size induce increase of computational cost. An optimal time step size is one that maximizes accuracy while minimizing computational effort.
In this paper, a new adaptive time-stepping procedure for dynamic limit analysis is suggested to calculate the optimal time step size. Three posteriori error estimators are used for control of time step size. The local velocity error estimator proposed by Zeng, Wiberg and Xie is applied for the assessment of the error by discretization of time domain. In dynamic limit analysis, it is assumed that the material is perfectly plastic in time interval. Due to this assumption, two types of error estimator are newly proposed for evaluation of the error of strain energy increment.
Numerical simulations have been carried out in order to verification of proposed adaptive time-stepping procedure. For each analysis, result with relatively small and fixed size of time step is assumed to be exact. Results from adaptive time-stepping are compared with results using same number of time step. The analysis results demonstrate the efficiency of the adaptive time-stepping procedure suggested in this paper.
