Localization and Propagation of Instabilities in Long Shallow Panels Under External Pressure

This paper discusses the response of long, shallow, elastic panels to uniform pressure loading. Under quasi-static conditions, the deformation of such panels is initially uniform along their length, and their response has the nonlinearity and instabilities characteristic of shallow arches. Shallower panels deform symmetrically about the midspan and exhibit a limit load instability. For less shallow panels, the response bifurcates into an unsymmetric mode before the limit load is achieved. A formulation and a solution procedure are developed and used to analyze the response of such panels beyond first instability. It is demonstrated in both cases that following the first instability the deformation ceases to be axially uniform and locqlizes to a region a few arch spans in length. A drop in pressure accompanies this localized collapse and causes unloading in the remainder of the panel. Subsequent deformation is confined to this region until membrane tension arrests the local collapse. Further deformation can occur at a constant pressure and takes the form of spreading of the collapsed region along the length of the panel. The lowest pressure at which this can take place (propagation pressure) can be significantly lower than the pressure associated with first instability.