Force vs. Displacement calculation 1

[jongyonkim]

Hi,

I am trying to model the force vs. displacement behavior of a thin sheet of silicon.

The four corners of the square sheet are fixed using a boundary condition (U1=U2=U3=0). I am to apply a point load in the center.

I would like to obtain a graph of this load force vs. downward displacement of the center.

What is the best method to do this?

1) I could specify a load force and see how much the center displaces (eventually displacement saturates to a steady value), but this would only give me a point on the graph; I would have to do this a hundred times to get a plot (which is not practical)...Is there an easier way of doing this?

2) I tried to vary the force with respect to time by defining a linear amplitude, but the results don't quite match the discrete data points produced by method #1 above...(I guess the structure isn't given enough time to stabilize its final displacement per given force, which varies continuously)

3) I'm also thinking of using the energy method. I set a velocity boundary condition at the center to get linear displacement. Then I obtain ALLWK, ALLKE and U3 (downward displacement) from history output, and use the following function in the "Operate XY data" to get force:
differentiate(combine("U3","ALLWK"-"ALLKE"))
Is this a valid way of measuring force? Since work is the integral of force with respect to distance, I can solve for work by differentiating the internal energy (ALLWK-ALLKE) with respect to displacement. Does this work?

Thank you in advance.

 

[bfillery]

Dear jongyonkim

I think you can specify the force at the centre of the plate as suggested. In a linear analysis, if you specify a fixed time stepping procedure and request a history output record of the required displacement at each substep, then a force displacment curve can be constructed as the percentage of the force at a particular substep will correspond to the percentage of the substep time to the total step time. Similarly for a nonlinear analysis, though non linear geometry should be turned on and automatic time stepping implemented. However, the procedure remains the same as that for a linear analysis.

bfillery

 

[jongyonkim]

Hi bfillery,

Thanks for the suggestion.

However, I forgot to mention the fact that I am to use ABAQUS/Explicit. The step I use is "Dynamic, Explicit" and nlgeom is turned on.

The reason why I'm sticking with Explicit is due to a more complex structure (the plain sheet of silicon is a simplified representation of the actual structure).

I would like to know what is the best/accurate method for measuring force vs. displacement under Explicit.

Thank you.

PS. I am also to simulate how the structure handles on its own weight (no force but gravitational). How do you "simulate" gravity? Apply a BC acceleration of -9.8 on the structure?

 

[bassmanjax]

Here's one way of doing it, assuming that you're interested in the load-displacement response in the U3 direction.

- Create an XY curve of the displacement at the centre of the sheet. Might help if you had a node in an NSET at the centre. This then gives you the displacement vs time at the centre.

- Create curves of the reaction loads RF3 at the fixed edges. Then, sum these curves using the sum() function in 'Operate on XY Data'. This will create a single curve of total RF3 vs time.

- Operate on these two curves using the 'combine()' function to create a single load-displacement curve. Job done.

Regards

Martin