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.
The calculation was based on the third order theory assuming linear-elastic material behavior (Error threshold 0.01 %). In order to illustrate the influence of the arc length on the numerical result as well as to show two possibilities to control the end of the calculation, three FE simulations with different specifications for the non-linear system analysis were performed.
|Settings:||Case 1||Case 2||Case 3|
|Control:||Load fact. = 1||Load fact. = 1||1. Bifurcation point|
|Initial arc length:||0.1||auto||0.1|
|Iterations per arc length:||3||3||3|
As illustrated in the figure below, all load-displacement curves calculated with the arc length method are in good agreement with the results of Sabir and Lock. (identical result curve for case 1 and 3 until first branch point is reached, load factor = 0.53) In addition, it becomes clear that a sufficiently small arc length is required for a detailed resolution of the complete equilibrium path.