COMPARISON of ANALYTICAL and FINITE ELEMENT SOLUTIONS of LOW VELOCITY IMPACT PROBLEM for SIMPLY SUPPORTED BEAM

Abstract

The aim of this study is to compare the results obtained from analytical and finite element solutions of low velocity transverse impact problem of a sphere onto simply supported beam. Twelve models with various mass ratios were created by keeping the beam dimensions constant and changing the sphere radius. The effect of the element size in the finite element solution was analyzed with five separate meshes whose element size gradually decreases at the impact point. In the solutions, the deflections of the beam and the displacement of the sphere at the impact point were taken into account. To check the validity of the model, a comparison with an experimental study in the literature was also made. Comparisons show that the deflections obtained from the analytical solution are compatible with the finite element solution within the period of repetitive or continuous contact between the sphere and beam. Particularly, as the mass ratio defined for beam and sphere gets smaller, maximum deflection values obtained from analytical and finite elements become closer. For the cases including sub-impact, after the sphere leaves the beam there exist differences in the results mainly because of the sub-impacts.