Abstract
We study the contact problem of a semi-circular ring indented by a rigid flat plane using the finite element and finite difference methods to investigate the equilibrium path (load–displacement relationship) and contact response. By comparing the results from different approaches, we verify the consistent equilibrium path and the two conditions where the contact mode changes and snapping occurs. We show that the transition condition of the equilibrium path from point to line contact agrees with the analytical solution based on the elastica model. In addition, We present the contact pressure distributions in detail using the finite element method. The results reveal that at the snapping point, the load decreases rapidly, whereas the local contact pressure significantly increases. These findings could offer rational design guidelines for curved elastic elements under out-of-plane compression.
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