I am looking into the four-point bend test, such as one in this YouTube video.

Sample screenshot from the video illustrating the problem: enter image description here

I am a little confused as to how the loads are prescribed numerically as boundary conditions. My intuition tells me that the object has to have a Dirichlet BC somewhere. But it appears that the 4 supports (2 on top and 2 on bottom) exert the vertical loads, hence they should be all Neumann BCs.

Am I thinking about this incorrectly?

  • 3
    $\begingroup$ The forces you show at the bottom of the beam are modeled as Dirichlet BCs; y-displacement equals zero at both points and x-displacement equal zero at one of the two points. $\endgroup$ May 22 '18 at 11:20
  • $\begingroup$ Oh hmm. Why aren't both x-displacements at the bottom zero? If only one is zero, then it seems we would lose symmetry? $\endgroup$
    – user27504
    May 22 '18 at 12:53
  • $\begingroup$ The x-displacement at one point is required to restrain rigid body motion in that direction. But, it is permissible to set x-displacement equal zero at both points. $\endgroup$ May 22 '18 at 13:27
  • $\begingroup$ Ah I see. Would you expect the results from a simulation to differ significantly when setting both points' x-displacement to zero or just one one of them? $\endgroup$
    – user27504
    May 22 '18 at 13:40

You could also take advantage of the symmetry of the problem. As an added advantage you end up with a mesh with half the elements.

I would just consider half of the beam and add roller constraints on D and also on the midplane of the beam, as presented in the following schematic.

enter image description here

This represents a mixed boundary condition in D. Horizontally, it has prescribed zero traction, and vertically a prescribed displacement of zero..


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