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

masarati at aero.polimi.it masarati at aero.polimi.it
Thu Jul 15 14:42:37 CEST 2010


> 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.



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