Rigid body modes 9

[idly123]

Hi all,
Can nay body clear me with he following questions:

a)Does Their exisist any relation ship between rigid body modes and boundary conditions?
b)Is it in any way also related to numerical integration points?
c)When all do we encounter an Zero energy mode?

Thnks in advace
regards
raj

 

[Spirit]

Hi DrRaj.
As asked in your message:
a)yes: you have a rigid body mode when your boundary condition does not fully restrain your model.
b)it is more exactly related to a singularity in the stiffness matrix.
c)when deformation exists that do not involve strain in your structure (=rigid body mode, that is a displacement that does not involve a deformation).

Hope to be af any help...cheers

Spirit
'Ability is 10% inspiration and 90% perspiration.'

 

[zuardy]

Hi,
I agree with spirit, so :
a)the structure will have 6 rigid body modes if it is fully unconstrained.
b)the singularity leads to very low eigenvalue.
To my know, the Phenomenons related to numerical integration points are shear locking and hour glass.
c) no more comments

cheers

 

[GregLocock]

The reality is that any mechanical system has at least 6 rigid body modes, in this universe. If your system does not appear to have 6 0 frequency modes, then it is a subsystem. In the less realistic case where we consider the foundation to be infinitely stiff and of infinite mass, then your subsystem's RBMs are controlled entirely by the constraints that exist between the foundation and the subsystem. It is perfectly aceptable to eliminate RBMs by adding appropriate constraints so long as you acknowledge that you have changed the model.

The typical error is to pin joint two or more points to the foundation (it's nice to have infinitely rigid reinforcement, but how often do you get it in practice?)



Cheers

Greg Locock

 

[Dinosaur]

Greg,

I am a bridge engineer. We try to avoid rigid body modes. The earth has adequate mass to suit me. Regards

 

[GregLocock]

Consider the simple case of the first bending mode of a rigid uniform bar in a planar world. If you constrain the ends with pin joints to suppress the X Y and RZ rigid body modes then do you also affect the frequency of the first bending mode?

Which way does the frequency move?

Given that you have added stiffness (ie additional constraints) to the system does that surprise you?

Do you understand why ? Cheers

Greg Locock

 

[idly123]

we say 6 independent DOFS , but when it comes to rigid body modes we say it as wether linearly dependent or independent...its really confusion...as to how exactly we decide that a given structure with a set of BCs will have these many linealy independent modes and these many dependent modes
please help me
raj
Raj
Structural Engr.

 

[zuardy]

Dr. Raj, don't be confused with DOFs in rigid body modes. There are the global DOFs for a rigid body so it is exactly 6 independent DOFs for each free body but a discretized body (FEM model) can have thousand or million of DOFs and the eigen modes of such body are of course so many as its DOFs.A mechanical system has actually at least 1 rigid body mode (consider a thrus element freed only in one DOF). If it has more then 6 rigid body modes, then it has a sub structures or parts that are not fully constrained (attached) to the main structure, any comments?

regards

 

[prost]

DrRaj:
While 6 Rigid Body Modes (RBMs) exist in 3D, meaning that these 6 modes must be constrained, there are only 3 RBMs in plane stress/strain (x-disp, y-disp, and z-rotation). If you construct a finite element matrix K (in the Ku=F) either by hand or by computer, you'll see that in 2-D you have N equations (that is, N degrees-of-freedom) and N-3 independent equations. If you try to invert that K, K is singular, so you'll get an error. Same thing happens when using somebody else's FE code--in 2-D you have to constrain at least 3 degrees-of-freedom (DOFs), in 3-D, at least 6, to invert the K matrix without error. The boundary conditions (BCs) are used to model the real structure as well as possible, but the BCs are also needed to eliminate the 3 or 6 RBMs.

s

 

[idly123]

I wish u all can have a look at Page Number 190 of the book by RD cook, Malkus and palsha on concepts and applications of feA. tHIS deals with element mesh and instabilities. This is zero energy mode. I wish u can help me with my question after having gone through this section. because i got confused only after reading that . May be some one among u can make a sense.
regards
raj Raj

 

[jstegmann]

Hi,

I just want to make a comment regarding the original point b).

As zuardy points out, numerical integration has to do with hour-glass modes, which are in fact zero energy modes resulting from an insufficient order of numerical integration (in the Gauss quadrature).

Many shell and plate elements employ reduced or selctive integration schemes to counter shear locking but the down-side is that this introduces zero energy modes (requiring hour-glass stabilization). It is hard to predict when we will encounter such modes, but the phenomenon is quite clear to identify, when you see it.

That's the best I can do in such a short space...

Cheers,

jstegmann.