 # Force - Displacement relationship from Ansys (Structural Analysis)

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• Last Post 13 May 2020
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rfn123 posted this 11 May 2020

Hi all,

I have a structure with springs where a part shows displacements when force is applied. Ideally, I would like to obtain the relationship between force and displacement, such that if I measure the displacement, I can derive the forces and moments acting on this structure at a given point.The result would be a matrix M, with F = M*x -- F being a 6D vector with forces and moments along the xyz axes and x the 6D displacement.

For the first step, I did a static structural analysis with Ansys. I have some questions regarding the next steps,

1) Does Ansys already provide such a force/moment-displacement relationship?

1) Can Ansys output the displacement in 6D instead of just x-y-z?

2) In theory, is the matrix I want to obtain the global stiffness matrix?

I am a bit stuck right now and would appreciate any kind of help or advice! Thank you!

peteroznewman posted this 13 May 2020

Consider a remote point on the end of a cantilever beam. F is a vector that loads that remote point with 6 loads: (Fx,Fy,Fz,Tx,Ty,Tz). Create six unit load models to exercise each of the degrees of freedom, one at a time. The six models have F setup like this:

• (1,0,0,0,0,0)
• (0,1,0,0,0,0)
• (0,0,1,0,0,0)
• (0,0,0,1,0,0)
• (0,0,0,0,1,0)
• (0,0,0,0,0,1)

Solve each model to determine the unknown x displacement vector with 6 elements in it, (x,y,z,Rx,Ry,Rz).

The diagonals of the stiffness matrix M are: 1/x, 1/y, 1/z, 1/Rx, 1/Ry, and 1/Rz. There is more work to get the off diagonal terms of the stiffness matrix.

The above example applied loads and measured displacement. You could also apply unit displacements and measure reaction forces and torques.  In either case, you must scale the forces and torques (or displacements and rotations) so as to maintain small deflections. I expect you want a linear approximation. If you want it to work for general large deflections, then things are more complicated.

I'm going from old memories in relating the ideas above. Consult an FEA theory textbook for the derivation of the stiffness matrix for a beam element, since that element has a node at the end that has exactly 6 degrees of freedom. If you type "beam element stiffness matrix" into Google, there are several results including some YouTube videos you can watch.

rfn123 posted this 13 May 2020

Thank you for the very helpful answer! Yes I am indeed assuming a linear approximation.

I stil have a question though:

In Ansys, how do you measure the displacements? In my understanding displacement is not quite the same as deformation, plus the deformation solution does not provide rotations. I was thinking about probing position, but position can only be scoped to rigid bodies according to the docs....

EDIT:

Okay I discovered the deformation probe which can be located to a point and measure the displacement. Close 