evaluation of internal force with known displacement field (FEA)

[Mingwu Li]

Hi all,

I am trying to evaluate internal force with known displacement field. I found that we can extract stiffness matrix from chrono. In addition, there is a function counting the number of evaluations of internal force calculation. I would like to plug in displacement fields and obtain the corresponding internal forces. Could you tell me what should I do to get that?

Thanks,

Mingwu

[Alessandro Tasora]

Dear Mingwu,

some hints here: I would split the problem in two parts: 1) computing FEA internal forces , 2) assigning a prescribed displacement

1) computing FEA internal forces

There are various options.
The most immediate is calling  ChSystem::LoadResidual_F(ChVectorDynamic<>& R, const double c)  with c=1, as

mysystem->LoadResidual_F(R, 1.0);

Keep in mind, your R vector must be sized as the n. of variables, ex. use mysystem->GetNcoords_v() to get this number in advance.
The issue with this method is that it stores _all_ forces in R, both external and internal. If you have no gravity, no loads, etc. etc., then it could be fine anyway.

Otherwise, you could call   ChMesh::IntLoadResidual_F(const unsigned int off, ChVectorDynamic<>& R, const double c) with c=1, and with the proper offset, where offset is 0 if the mesh is the only thing you added to the system, otherwise -for example- if you added two bodies and a mesh to the system, offset is 6+6=12, etc.

This IntLoadResidual_F is a low level function, that stores in R  only the internal loads of the finite elements added to mesh, at current state, so external loads are not stored in R.

Also note: set R to zero before calling LoadResidual_F  because these "Load..." functions do a += operation, they are incremental.

2) assigning a prescribed displacement

This is not so obvious: in Chrono there are corotational FE and other types of FE, so "displacement" can have different meanings (local, total, etc.), but I am sure you can do whatever you need by using the two following functions, that allows you to set the system in a configuration state, or to get the current state (you can get the state, increment the DOF you want, store it again, call IntLoadResidual_F(), etc.)

ChSystem::StateGather(ChState& x, ChStateDelta& v, double& T)     here only the x part is relevant to you - positions and rotations, v contains speeds, T is time

ChSystem::StateScatter(const ChState& x,  const ChStateDelta& v,  const double T,  bool full_update)

Note, if you need to increment a state x by some dv, instead of doing  xnew=x+dv, rather use

ChSystem::StateIncrementX(....)

because it is the most general way that accounts also for the cases where the size of x is different from size of dv because   x contains rotations in SO3 as quaternions (4 scalars) whereas dv contains rotation vectors  or other so(3)  Lie algebra stuff (3 scalars).

regards

Alessandro Tasora

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