Effect of Initial Imperfections on the Instability of a Ring Confined in an Imperfect Rigid Boundary

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Abstract
The stability of a radially constrained, complete, circular ring subjected to thermal stress and of a similarly restrained portion of a circular ring under circumferential end load is investigated. The effect of three types of initial geometric imperfections on the buckling behavior is determined. Results obtained, employing shallow arch approximations, show that this behavior depends on the assumed form of imperfection. In one case, no bifurcation or limit point exists at finite load level; in the second case, bifurcation and snap buckling may occur; in the third case, the system admits of a limit point. A design curve is proposed which can be used to estimate the stability limit of a circular ring exhibiting a certain “out-of-roundness.”

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