What is a RBE3 element?
Altair EmployeeAnswers
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Altair Forum User said:
I got partial answer stating it is interpolation element.but what sort of? Please explain.
everyone says it is interpolation element, but actually it is not an element, it's just a system of equations which constraints DOFs of nodes
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it is interpreted as element at the pre and postprocessor and couple DOFs...
;-)
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Hope it will help you:
The interpolation elements allow you to model the motion of one or more grid points as a function of the motion of the other points. The RBE3 writes equations typical for interpolating the motion of points on a surface or in a volume to one grid point, and the RSPLINE uses the equations of a beam to write constraint
equations.
Here are examples of modeling an interpolation function. Suppose that there are four grid points at the vertices of a square surface and a fifth grid point is to have the average of the motion of all four points.
If you want the motion of grid point 100 in the x-direction to be the average displacement of grid points 1 through 4, use the following:
Average displacement u100x = x1 (u11 + u21 + u31 + u41)
A similar equation is used in the T2 direction. X1 and X2 are unknown quantities to be determined. By inspection, if the desired motion for point 100 is the average of the motions of points 1 through 4, the Xi are the inverse of the sum of the (implied) unit coefficients on points 1 through 4, or
X1 = X2 = 1/4
The following MPC entry provides this action in the T1 direction:
1 2 3 4 5 6 7 8 9
10
MPC 10 100 1 -1.0 1 1 0.25
2 1 0.25 3 1 0.25
4 1 0.25
The minus sign occurs because the MPC equation requires that all terms of the equation be on the left-hand side and equates them to zero. The first DOF listed on an MPC entry is always the dependent DOF.
Since a constraint equation may be multiplied by any arbitrary nonzero term without changing its meaning, let us multiply the entry for the T2 direction by 4.0 to reduce the labor of input preparation. The action in the T2 direction is exactly the same regardless of the term used to multiply all coefficients.
This entry is then written as follows:
1 2 3 4 5 6 7 8 9
10
MPC 10 100 2 -4.0 1 2 1.0
2 2 1.0 3 2 1.0
4 2 1.0
It can be shown that the MPC equations form the matrix equation
{um} = [Gmn] {un}
From principles of energy conservation, these constraint elements enforce a relation among the constraint forces qi of the form:
{qn} + [Gmn]T {qm} = 0
In the example above, the equation on ui above implies the following relationships among the constraint forces. If a force is applied on the m-set degree of freedom such that q1001 = 1.0, the resulting n-set forces are
q11 = q21 = q31 = q41 = -0.25
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When I create RBE3 then click Review, I see some information on leg nodes of RBE3.
1. Node Number - ID nodes
2. Constraint dof
3. Sometimes it is '0', Sometimes it is '1'.
Could you explain what is the meaning of '1' or '0'?
Thx.
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I think you are pointing to weighting factor. Please share image for better understanding. Meanwhile, I am sharing an image with explanation of RBe3. May it will be helpful.
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