The low velocity impact between a steel ball and an ellipsoidal shell is simulated by using the finite difference method. The displacement field in a control volume is approximated with the displacement vectors at the neighboring nodes in the control volume in terms of Lagrangian interpolating polynomials. The approximated displacement field is differentiated to obtained discretized dynamic equations by applying the weighted residual method on each control volume. A domain transformation is used from the ellipsoidal brick to a Cartesian brick.
The contact force and area between the two bodies are modeled by the Hertzian contact theory. The resulting nolinear equations are solved by the Gear algorithm in IMSL.
The impact by a steel ball on a glass panel is solved and the results are compared with those obatined by using degenerated isoparametric shell finite elements. A coarse and a refined mesh are tested. The overall trends and magnitudes of the displacement responses match relatively well with one another, but the detail histories are found somewhat different, especially along the time coordinate. The propagation of displacement wave, however, is seen well describable by the present formulation and models. It is conjectured that the mesh used is still too coase to examine the local stress distributions in the neighborhood of the contacting area.