[MBDyn-users] Basis Functions and Test Functions??

David Cross (Civ, ARL/VTD) david.m.cross2 at us.army.mil
Thu Jul 15 15:16:55 CEST 2010

masarati at aero.polimi.it wrote:
>> Thank you, that answers my question perfectly.  Something else that came
>> to mind...
>> In reading about this type of beam theory analysis in the past, I was
>> under the impression that it is most accurate for a frame of beam
>> elements which is long relative to its other dimensions, such as a
>> helicopter rotor blade.  Should I be worried with the accuracy of the
>> beam analysis if I am using a lattice of beam elements, which do not
>> make up long and slender frames??
> David,
> on the contrary, the beam element implemented in MBDyn is based on
> Timoshenko's theory for thick beams.  As such, it works fine for
> relatively thick beams (i.e. non slender), provided you can figure out
> appropriate coefficients for the shear stiffness terms.  The 3-node
> element does not suffer from shear locking.  The 2-node element suffers
> from some residual shear locking, which can be alleviated by modifying the
> stiffness coefficients according to the formula presented here
> <http://www.aero.polimi.it/~masarati/MBDyn-input/mbdyn-input-1.3.13/node47.html#SECTION001261700000000000000>.
>  For a diagonal stiffness matrix, it boils down to correcting shear terms
> GA_y and GA_z as
>     GA_y = 1/(1/GA_y + L^2/(12*EJ_z))
>     GA_z = 1/(1/GA_z + L^2/(12*EJ_y))
> Cheers, p.
Thank you.  That is helpful to know.  I guess up to this point I have 
been defining a diagonal matrix without any consideration towards 
correcting the shear terms.  Once again, I appreciate the help and advice.


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