Stochastic Applications in Crashworthiness

Abstract

Due to geometrical, and material property variations, response of any structural member varies from the nominal design value. Typically the geometrical and material variations are the resultant of manufacturing variations. In this paper, the effect of these variations about the nominal values on structural response is studied using stochastic or probabilistic methods. Circular aluminum cross-sections are becoming popular in structural energy management applications. Also, significant research has been done to estimate the mean crush load for a circular section using empirical relations. An empirical relation, which is a function of thickness, outer radius, elastic modulus and yield strength, was used to estimate the mean crush load. Based on the measured thickness, outer radius and yield strength, the mean crush load is calculated using the empirical relation. Also, using the empirical relation, the variation in the mean crush load is estimated using linear statistical approach and Monte-Carlo simulation. In both the stochastic methods, actual mean and standard deviations of thickness, outer radius and yield strength are used. Also, using the extreme variations of these factors, mean crush load is predicted using an implicit Finite Element Analysis (FEA) code. The FEA prediction is in good agreement with the results of the testing. However, the designed mean crush load based on the empirical relation overestimates the crush loads by about 11%. The results of the study showed that the tube thickness and yield strength variations significantly affect the crush loads. Based on the Monte-Carlo simulation and FEA values using the extreme values for the geometrical and mechanical properties, one can design crash structures that take into account the inherent variability of components.