The Effect of Residual Damage Interpolation Mesh Fineness on Calculated Side Impact Stiffness Coefficients

The subject study presents the results of an investigation into the effects of the level of mesh fineness used on the calculated test vehicle b_1-Campbell and CRASH3 A and B stiffness coefficients based upon FMVSS 214D compliance and high-speed lateral NCAP assessment tests. An analytical method is presented based upon a matrix implementation of the existing CRASH3 formulation that allows for the rapid evaluation of all iterations of the equally spaced formulation based on the number of measured crush values present to the front face of the side-impact moving deformable barrier {N: 2 ≤ N ≤ 17}. This formulation accounts for the necessity for aligning the nodes used in the discretization of the direct damage regions of the test vehicle and the moving deformable barrier for the zonal implementation of the force balance method. The efficacy of the calculated stiffness coefficients, based upon the level of mesh fineness utilized, was gauged by reconstructing the a priori known moving deformable barrier impact velocity vector. A general trend of decreasing stiffness coefficient magnitude was observed with increasing levels of mesh fineness when compared to the coarsest mesh however this trend was not always present with successive increases of mesh fineness for all vehicles. This finding was echoed in the reconstructed moving deformable barrier impact speed. The reconstructed moving deformable barrier angulation was exactly matched regardless of the level of mesh fineness used. These results point to the importance of the application of sound engineering judgment on the appropriate level of mesh fineness needed for specific reconstructions. An evaluation of the total population of test vehicles evaluated (98 passenger vehicles) was conducted for the purposes of trend analysis. Compliance and assessment tests were pooled (p > 0.09 for all N for all coefficients; single factor ANOVA). Statistically significant differences were found between tests (df = 97; p < 0.0001) and within the levels of mesh fineness used (df = 15; p < 0.0001) for all stiffness coefficients (1 way ANOVA with repeat measures). This finding was replicated for the mean relative difference with respect to the known pre-impact moving deformable barrier speed with the mean difference approaching zero for all levels of mesh fineness N ≥ 5, however the individual vehicle variability was evident based upon the ± 10% standard deviation. Finally, the correlation between test vehicle wheelbase and the stiffness coefficients was tested formally using the Pearson correlation. Both the b_1-Campbell (-0.64 ≤r≤ -0.57 for all N; p≤ 0.0001 for all N) and CRASH3 B (-0.38≤ r≤ -0.35 for all N; 0.0001≤ p≤ 0.0004 for all N) stiffness coefficients were negatively correlated with test vehicle wheelbase. The CRASH3 A stiffness coefficient was not correlated with test vehicle wheelbase (0.00 ≤ r ≤ 0.09 for all N; 0.3637 ≤ p ≤ 0.9811 for all N). The population of test vehicles was subsequently categorized based on the existing CRASH3 wheelbase categories and the mean CRASH3 A and B stiffness coefficients, as functions of the level of mesh fineness used, were compared to the nominal stiffness coefficient valuations. Large relative differences were noted in the CRASH 3 A stiffness coefficient for all levels of mesh fineness. Small relative differences were noted in the CRASH3 B stiffness coefficient for all levels of mesh fineness beyond the coarsest meshes used.