Buckling of a Heated Ring Enclosed in a Rigid Case

We propose to solve the buckling problem for metal rings subjected to compression loading when externally enclosed in a rigid medium as a contact problem of deformation of a composite solid with a unilateral constraint. This method is based on manufacturing deviations characteristic of real structures; general state of stress; real-time operation. With this approach, the method makes it possible to determine the moment of local buckling of the ring visually and quantitatively from the changes in the stress-strain state of the ring. We implemented our method in the LS-DYNA software package in the dynamic formulation using solid finite elements. The geometrically and physically non-linear computation problem statement allows for taking large displacements and plastic strains into account. External compression loading of the ring is stated by its heating inside a rigid enclosing medium (the case), which is considered thermally insulated. We do not solve the heat conduction problem. We computed buckling parameters of a thin steel ring for two manufacturing deviation types relating to local variations of ring and case thicknesses at different lengths. We show how these two types lead to differences at the initial ring deformation stage and subsequent loop formation ("inward lobe"). We present strain field images for the ring and the case, which made it possible to visually detect the ring buckling moment. We plotted the stress, strain and displacement curves in the local delamination area. These curves enabled us to quantitatively detect the ring buckling moment. Qualitative and quantitative estimates of ring buckling matched

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