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GlobalStiffnessTimeStepper

 

Hi Bruno,

I was reading code of GSTS trying to write down what it computes. Do you
have some paper for reference?

1. Concerning per-body stiffness, we have diagonal terms of the
stiffness matrix Kii=(kn-kt)*ni²+kt. If I understand right, the
"rotational stiffness matrix" are non-diagonal terms of K, i.e. Kij=(ni²
+nj²)kt*r for i≠j. Summing rigidities of all contacts gives per-body
rigidity, that's clear.

Now, e.g. in  http://www.fisica.ufc.br/hans/p/256.pdf (please swallow
the fact that they use (1), that is not important now) eq. (16) gives
local rigidity proportional to

  (Kn N ⊗ N)+(Kt T^T T)

where N and T are projection tensors defined in (5).

Now, I am not able to make up my mind whether these two definitions are
equivalent (neglecting the difference kn vs. Kn). Can you enlighten me
on that?

2. If I see correctly, computation of timestep from rotational stiffness
is mathematically incorrect; e.g. line 39:
  
  dtx = sdec->inertia.X()/Rstiffness.X();

as it mixes up inertia.X() in local frame and Rstiffness.X() in global
frame. For spherical particles, that makes no difference, of course.

Cheers, v.




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