Rigid body modes
Rigid body modes
(OP)
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
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





RE: Rigid body modes
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.'
RE: Rigid body modes
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
RE: Rigid body modes
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
RE: Rigid body modes
I am a bridge engineer. We try to avoid rigid body modes. The earth has adequate mass to suit me. Regards
RE: Rigid body modes
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
RE: Rigid body modes
please help me
raj
Raj
Structural Engr.
RE: Rigid body modes
regards
RE: Rigid body modes
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
RE: Rigid body modes
regards
raj
Raj
RE: Rigid body modes
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.