Buckling of a pre-buckled shell

A flat shell was pre-buckled into a sine wave using ABAQUS by loading one of its edges in the x-direction. The shell was then squashed between two walls by moving the top wall down the y-direction and the further buckling behaviour was observed. The shell was made from shell elements in ABAQUS and the walls were analytical surfaces. A rectangular plate behaved in almost a 2D manner, buckling into higher and higher modes as the shell was squashed. Physically this resulted in more and more sine waves of smaller and smaller amplitude. The more interesting results arose when a hole was added to the centre of the plate and a 3D behaviour was observed. As the shells buckle into higher modes, the structure becomes stiffer. Similarly unloading results in a less stiff structure. Applications for these types of structures exist where a variable stiffness could be beneficial, such as in buildings or aerospace structures.