## Forum

### Negative Diagonal Stiffness terms for Curved Beams

1. Hello,

I had some difficulties while modelling curved beam. Some of the diagonal stiffness properties  of the section becomes negative after solving with VABS. The geometry that we are trying to model is the following;

-          Hollow tube

-          Ro = 0.0375m

-          Ri = 0.0325m

-          Material: Aluminum

-          Radius of the beam curve is 0.275m

-          90degree arc

The begining of the input file is as the following:

0 0

1 0 0

1 0 0 0

I calculated curvature as Angle/ArcLength. I also tried in mm instead of m.  Negative diagonal terms were still there.

If there is no solution to this problem, can you suggest a better way of modeling such an structure?

Best regards.

2. One student looked at your issue and he sees two seemingly separate issues:

1. There are might be something wrong with the input file, possibly regarding the geometry. Setting k3 = 0 in input file gives me unexpected results: for the symmetric cross-section you have, you ought to be getting identical values for the two shear stiffnesses and also for the two bending stiffnesses. For example, you have S_22 = 1.42 E+07 and S_33 =  4.797E+06, S_55 = 4.62E+10, S_66 = 4.65E+10. He independently wrote an input file and got S_22 = S_33 = 1.436E+07, S_44 = S_55 = 4.66E+04 (using SI units). Aside from using a finer mesh, the student used 8-noded elements instead of the 4 they did. It is likely you might have to re-do the mesh.

2. Given a corrected input file, the beam you’re looking at is highly curved: calculating “a k_3” (for a = 0.0375 x 2, k_3 = 1/0.275) gives 0.2727… and for that value we also got nonsense results. However, for example, if he change k_3 to a tenth of that value, he gets far better results. But the input file you provided generates negative stiffness values even for lower curvatures (where a k_3 = 0.02727.. ).

If you wish to have a look, the students input  file, along with the output files of 3 cases: prismatic, k_3 = 1/0.275 and k_3 = 0.1 x 1/0.275 are attached.