Buckling of a double sector thin elastic plate: Analytical solution

Analytical solutions for elastic buckling and post-buckling geometries are scarce. The present work presents such a solution for a sample geometry, initially planar, which buckles into a complex 3D shape under tensile load. The assumptions are that the sample thickness is small, so that flexural stiffness is low compared to in -plane strain stiffness, and hence the sample can be considered inextensible. The initial geometry is composed of two disk angular sectors sharing a common edge. Under tensile loading, the two radial edges of each sector tend to align so that each half turns into two regular cone sectors. As the tensile load increases, the cone angle progressively decreases, but the same generic form holds the sample extension all along the tensile direction. Such a solution may be useful for validating numerical simulation tools, or stereo-vision shape measurement procedures.