Since the mid-80's, the explicit finite element method using a contact algorithm based on the penalty method has achieved significant success in automobile crash analysis, sheet metal forming and other impact engineering. As the finite element analysis method has been incorporated into the design and manufacturing analysis process, its reliability becomes increasingly important. This paper presents a simple example of a loaded string over an obstacle, a Signorini type of contact problem with a complete analytic solution. The finite element solution is shown to converge to the analytic solution with uniformly refined meshes. The penalty method for contact also converges to the rigid constraint condition. The convergence rate of some items of interest matches the available theoretical assessment. The study is extended to the high speed crash of structural components with large plastic deformation. The convergence behavior of the component crash will be discussed, with situations before and after contact occurs.
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