|
|
||
|
|
|
|
from the website:
http://www.smr.ch/local/doc/B2000++/test_cases/ch03s02.xhtml
The authors (anonymous) of the web site write:
"This test case is a variant of the panel described by Verolme [1] and Remmers [2]. The panel illustrates the post-buckling behaviour of an initially undeformed panel, which 'jumps' from its pre-buckling state to a stable post-buckling state. Remmers [2] simulates the behaviour by preforming a dynamic (transient) analysis at a load just after the instability point, following the mode-jumping technique according to Riks and Rankin [3, 4].
The term mode jumping is often used to describe a sudden dynamic change in a static process. In computational mechanics, the abrupt change in wave numbers (such as from pre- to post-buckling state) is indicated as a mode-jump. This phenomenon was first mentioned by Stein [5], describing a buckling experiment with a flat panel. Mode-jumping is an important phenomenon for stiffened panels, where a mode-jump may occur from local skin buckling (between the stiffeners) to a global buckling pattern.
In order to simulate such jumps with FEA, one can use a transient solving routine including some form of damping, such as Rayleigh damping, in order to find a stable static path [2]. The artificial damping scheme of B2000++ allows for finding a stable path with 'static' analysis. This test case uses this artificial damping method to find a stable post-buckling solution (an undamped simulation will fail).
The panel is made out of 2024-T3 aluminum and simply supported at the straight edges and clamped at the curved edges. The panel is compressed at one of the curved edges, creating an edge shortening of 3 mm.
The slide shows the deformed panel and the load-shortening curve of the analysis for a 160x160 mesh and the load-shortening curves for other mesh densities.
References:
[1] K. Verolme. The development of a design tool for fiber metal laminate compression panels. PhD thesis, Delft University of Technology, 1995.
[2] J. Remmers. Mode jumping with B2000. Master's thesis, Delft University of Technology, 1998.
[3] E. Riks, C. Rankin and F. Brogan. On the solution of mode-jumping phenomena in thin-walled shell structures. Computer Methods in Applied Mechanics and Engineering 136, pp 59-92, 1996.
[4] E. Riks and C. Rankin. Computer simulation of the buckling behaviour of thin shells under quasi-static loads. Archive of Computational Mechanics in Engineering 4, pp 325-351, 1997.
[5] M. Stein. Loads and deformation of buckled rectangular plates. NASA Technical Report, National Aeronautics and Space Administration, 1959.
Page 52 / 444