On Symmetric Buckling of a Finite Flat-Lying Heavy Sheet

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Abstract
An elastic sheet with non-negligible density and finite length lies horizontally on the ground. The ends are clamped and subjected to compressive forces. Depending on the force, the sheet may be regarded as “long” or “short” with different characteristics. The critical buckling load, redefined as the force below which the sheet will always return to the horizontal state under any finite disturbance, is higher than the Euler buckling load of a weightless sheet. When deflections are small and finite the sheet is stable for given end displacement, but is unstable for given force. Approximate analytic solutions compare well with the results of exact numerical integration.

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