Roll up beam cantilever

Problem definition

To show the ability of the co-rotational beam element to handle large rotations the following example describes a roll up beam structure. For that purpose a cantilever of the length L = 1.00 is loaded with a linearly increased z-moment at its tip. The structure is discretized with 100 elements, E = 210E09, ν = 0.30, A = 0.01 and Iz=Iy=IT = 0.00001.

Statical System [1]

Results

The beam will form one total circal as soon as the curvature is κ = 1/R = 2π/L = 6.283 and therefore the z-moment equals M_z = κ*EI_z = 1.32E07.

Roll-up beam struture: Z-Moment

References

1. Steen Krenk. Non-linear modeling and analysis of solids and structures. Cambridge Univ. Press, 2009., pp. 114-115.