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# Prof. Yu's Research Group in the Cloud

## Forum

### GEBT parameterization for initially curved composite beams

1. Hello,

I am working with GEBT and VABS to model a 3D composite curved beam (see 3D_beam_Abq.png) as an equivalent beam, the goal is then to compute the deformation of the equivalent beam when it is submitted to a concentrated load at its tip.
The first step is to use VABS to determine the section properties of the curved beam. The input files for this step are given in "VABS_section_analysis/".

The second step is to use these section properties (the compliance matrices especially) to compute the deformation of the equivalent beam submitted to a concentrated load. For this second step, I used the GEBT software. I considered a 3D FEA computation realized in Abaqus (see 3D_beam_Abq.png) as a reference for the beam's tip deflection. I was not able to retrieve the same value with Abaqus and VABS/GEBT for the tip deflection value.

To set up my GEBT computation, I defined two nodes both located on the x axis (x1 = (0 0 0) & x2 = (0.26 0 0)). Between these nodes, I defined 16 beam elements which are associated to a frame, a material and a curvature. The curvature has been determined from the 3D geometry ( same as for the VABS computations). The selected frame is the global frame, because the two nodes of the beam are aligned with the global X axis. Finally the material properties have been extracted from the VABS analysis, there are two sections matrices (which are very similar) for each one of the beam's nodes. To understand this computation, one must know that the VABS computation has been performed in millimeters (otherwise the computation crashed), whereas the GEBT computation was realized in meter. To do so, I simply converted the curvature and the Timoshenko compliance matrix into the right units.
My GEBT input file is given as "GEBT_input.dat", and when I run it, the GEBT_input.dat.out is created. In this file, we can see the nodes initial coordinates and displacement and also the elements initial coordinates and displacements. But when I plot the initial position for the nodes and the beam elements, there is an inconsistency. The nodes have got the right position but the generated beam elements do not. Because of the curvature, the beams's Z coordinates are decreasing and the last beam elements does not match the second node x2 specified in the input file. I plotted in "beam_inconsistency.png" the nodes position, the generated inconsistent beam elements and the beam elements I was actually expecting. The definition of the geometry is not very clear to me in cases with initial curvature. Could you please give me some guidelines to properly model a beam with initial curvature ?
Also, I was wondering if you could provide me some validation cases between Abaqus (3D model) and GEBT for initially curved beams ?

Best regards,
Antoine

1. Hello,

Did anyone had the chance to check my post ? Is my problem well explained ? I currently have a trial license for the VABS software and I would like to understand how to model initially curved beam before my license expires.

Best regards,

Antoine

2. It is easy to do the cross-sectional analysis for initially curved/twisted beam. You just need to input the initial curvatures. Indeed it will be slightly more difficult to model it using GEBT and we have to use it to generate the 1D geometry. Can you use a few slides to clearly describe the problem and how did you get the numbers to put to GEBT.

1. Dear Dr Yu,

Thank you for the answer, I will try to explain my problem more clearly. My problem is not with VABS, I am able to run sectionnal analysis with VABS for initially curved beam. What I can't do yet is to use the section information in GEBT. Actually, I don't see how to properly defined a curved beam with GEBT.

Firstly, I will detail the beam I want to study in GEBT. It is a curved beam defined between two nodes (denoted node1 and node2), both located on the x axis. This beam is represented the attached picture "Curved_beam_definition.png". In this picture, we can see the beam's nodes, which are both located on the X axis (the coordinates are written on the plot). My goal is to define a curved beam between theses nodes. On this plot, I displayed the curved beam elements I would like to generate (the red curve on the plot) and I also plotted the same beam elements without curvature (the green curve on the plot).

But I am not sure how to define these curved beam elements in GEBT.To define them in my GEBT input file (called 'GEBT_input.dat'), I simply defined my two nodes (with the coordinates given in the plots) and a member between them. Then I specify the discretization (16 elements in my example) and the curvature of this element. But when I try this, it looks like the beam element does not match the nodes (node1 & node2).
To illustrate my problem, I have attached the picture 'curved_beam_elements_GEBT.png'. In this plot, we can see that the generated beam elements (extracted from the results file GEBT_input.dat.out) are not matching the two nodes defined in my input file. Would you have a GEBT case where a curved beam is studied ? If not, could you explain to me how can I properly define a curved beam in GEBT ?

Best regards,

Antoine

3. Hi Antoine,

I checked your input file and found there are two possible errors:

1. The unit of ncurv (curvatures), i.e. k1, k2, and k3, is "radian/meter";
2. The nframe section it should be the direction cosine matrix at the key point 1 (start key point). For your case, you can replace the current identity matrix with [0,0,1;0,1,0;-1,0,0].

Qi

1. Hi,

Thank you for the answer. I have checked the units of the curvature and it is correct. I am not sure to understand the second point because in my case, I want the beam to be aligned with the x axis, so I choose to use the global frame for the beam's local frame. It is why I use the identity matrix for the direction cosine matrix at the key point 1, I could have also specified this in the member definition (at line 8 : '1 1 2 1 2 0 16 1' instead of  '1 1 2 1 2 1 16 1' )

I had the chance to run computations without curvature which gave me good results, but when I define an initial curvature, I don't have good results. I think I am doing something wrong with the curvature. Would you have a clean case with an initially curved beam I could run. It would allow me to understand how to model my problem and explain more clearly what is not clear to me (with your input file this time) ?

Best regards,

Antoine

4. Hi Antoine,

Your current nframe input section is the reason for geometry. To be clear, in your input file, this section read:

1 # frame No. 1
1 0 0
0 1 0
0 0 1

The fix to get the expected geometry is to replace the above with:

1 # frame No. 1
0 0 1
0 1 0
-1 0 0

----------------------------------------------------------------------------------------------------

Here is why:

The nframe section should be the direction cosine matrix (DCM) between the local coordinate system (tangent vector) and the global coordinate system. at the beginning of a member (Key point 1 for this case).  Attached please find a sketch to explain this definition. The black c/s is global, and the red c/s is the local one. The DCM between these two frame is the new input I provided.

Qi

1. Hello,

Sorry for the late answer, I did not receive the notification e-mail from cdmHUB. Anyway, I think I understand how to set up my case now. Just to be sure, in the example you showed, the beam's radius of curvature is equal to half the beam's length, right ?

And in a case where the curvature would be smaller (aka the radius of curvature would be bigger), the rotation between the global c/s and the local c/s should be smaller ?

Best regards,

Antoine

5. Antoine, to receive email notification, you need to change your email setting on the right sight of the screen. Please let me know if you have difficulty to change the setting. See highlighted area on the attached screenshot.