Problem definition
The problem considered is the static geometrically non-linear pull-out of an open cylinder with a load P = 40,000. The geometry of the cylinder is defined by: L= 10.35, R = 4.953 and h = 0.094, while the isotropic linear elastic material is characterized by E = 10.5E6 and ν = 0.3125.
Problem definition [1]
The key displacement is the vertical deformation u_z at the point of load application as illustrated in the figure above, with the reference equilibrium path according to [1] included in the results below.
Results
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.
References
- 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.