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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?

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    $\begingroup$ 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. $\endgroup$ – Bill Greene 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. $\endgroup$ – Bill Greene 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
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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

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  • $\begingroup$ Why is a roller constraint added at D, when in the full problem, there is no restraint in that location? $\endgroup$ – user27504 May 25 '18 at 17:34
  • $\begingroup$ @user27504, in the experiment the beam is restricted to move vertically in D, that is what a roller mean. $\endgroup$ – nicoguaro May 25 '18 at 19:22
  • $\begingroup$ Ah I see. So numerically, at D, is it a combined displacement and traction boundary condition? $\endgroup$ – user27504 May 25 '18 at 19:35
  • $\begingroup$ @nicoguaro side note. where/how did you draw this nice figure? some LaTeX package? $\endgroup$ – Anton Menshov May 26 '18 at 1:54
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    $\begingroup$ @AntonMenshov, I used Inkscape. $\endgroup$ – nicoguaro May 26 '18 at 2:01

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