Roll up beam cantilever
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 = 210E9, ν = 0.30, A = 0.01 and Iz=Iy=IT = 0.00001.
Statical System
The following deformation (exaggerated) animation of the Kratos thin quad element (mesh = 192 elements) is provided for context.
Open cylinder pullout: Deformation of Kratos thick quad element
The results of the test for the thin and thick triangle Kratos shell elements (mesh = 3000 elements) are presented below.
Open cylinder pullout results: triangle elements
The results of the test for the thin and thick quadrilateral Kratos shell elements (mesh = 192 elements) are presented below.
Open cylinder pullout results: quadrilateral elements
Both graphs above indicate all Kratos triangular and quadrilateral shell elements agree with the reference solution.
- K.Y. Sze, X.H. Liu, and S.H. Lo. “Popular benchmark problems for geometric nonlinear analysis of shells”. In: Finite Elements in Analysis and Design 40.11 (2004), pp. 1551 –1569.