Snap Through Problem of a Cylindrical Shell

The cylindrical shell subjected to a central point load as shown below was first numerically investigated by Sabir and Lock in 1972. Their results are used to verify the arc length method implemented in InfoCAD. For the comparison calculation, the structure with jointed supports on two sides was discretized with 20x20 shell elements.

Discretization with supports, load and parameters
Discretization with supports, load and parameters

The calculation was based on the third order theory assuming linear-elastic material behavior.

In order to verify the influence of the arc length on the numerical result, two FE simulations with different specifications for the non-linear system analysis are performed.

Settings: Case 1 Case 2
Control, load factor: 1 1
Initial arc length: 0.1 auto
Up limited: yes no
Iterations per arc length: 3 3

As illustrated in the figure below, both load-displacement curves calculated with the arc length method are in good agreement with the results of Sabir and Lock. In addition, it becomes clear that a sufficiently small arc length is required for a detailed resolution of the complete equilibrium path.

Load-displacement curves
Load-displacement curves