Difference between revisions of "Contrib:KeesWouters/bc/rbe3"

Revision as of 21:54, 18 February 2013

Geometry and mesh of the block with cylindrical hole

This construction shows the RBE3 constraint. This is used to apply a moment to the top surface of a cylinder. The bottom surface of the cylinder is fixed 3dof to the world. The inner and outer diameters of the cylinder are 15 and 17 (arbitrairy units) and length 75. The used material is steel, material properties are in ISO units (this makes the dimensions of the cylinder ISO as well).

The geometrical entities on the cylinder are, A for surface areas:

• Atop and
• Abot

Abot is used to apply the torsion moment, Atop is used to apply the fixed boundary condition to the 'world'.

Some images of the construction of the geometry and mesh:

File:Kw cylinder rbe3 geom.png

*

The mesh is divided in 13 divisions in axial direction. In radial direction 6 divisions are present and in tangential direction two times 6 divisions are made. Later on we will modify this last mesh.

The centre 0D nodes is the master node to apply the constraint to the nearby surface.

Definition of node groups

Mcyl=DEFI_GROUP(reuse =Mcyl,
                MAILLAGE=Mcyl,
                CREA_GROUP_NO=_F(NOM='Nbot',GROUP_MA='Abot',),);                   

Mcyl=DEFI_GROUP(reuse =Mcyl,
                 MAILLAGE=Mcyl,
                 CREA_GROUP_NO=_F(NOM='Nmaster',GROUP_MA='Pmaster0',),);                   

Definition of node groups

CylModel=AFFE_MODELE(MAILLAGE=Mcyl,
                     AFFE=(_F(TOUT='OUI',
                              PHENOMENE='MECANIQUE',
                              MODELISATION='3D',),
                           _F(GROUP_NO='Nmaster',
                              PHENOMENE='MECANIQUE',
                              MODELISATION='DIS_TR',),),);

N_stmass=AFFE_CARA_ELEM(MODELE=CylModel,
                        INFO=2,
                         DISCRET=(_F(CARA='M_TR_D_N',
                                     GROUP_NO='Nmaster',
                                     VALE=[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.00,0.00,0.00]),
                                 _F(CARA='K_TR_D_N',
                                    GROUP_NO='Nmaster',
                                    VALE=[0.0,0.0,0.0,0.0,0.0,0.0]),),);

Since the node apparently does not have any degrees of freedom, we need to apply a discrete element MODELISATION='DIS_TR' to the master node Pmaster. This is an element that carries mass and stiffness, but all entities have been set to zero in the value assignment, see DISCRET and VALE in the statement above. Then effectively only a node with translational and rotational degrees of freedom remains.

The command part

DISCRET_F(CARA='M_TR_D_N',GROUP_NO='Nmaster',VALE=[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.00,0.00,0.00]),

defines:

• the mass properties M_TR_D_N for
• the node 'Nmaster' (a single node may to be applied to the GROUP_NO), and
• the VALE group defines the mass m and Ixx, Iyy, Izz, Ixy, Iyx and Izx and three eccentricities.

The command part

DISCRET_F(CARA='K_TR_D_N',GROUP_NO='Nmaster',VALE=[0.0,0.0,0.0,0.0,0.0,0.0]),

defines:

• the stiffness properties K_TR_D_N for
• the node 'Nmaster' (a single node may to be applied to the GROUP_NO), and
• the VALE group defines the stiffnesses Kx, Ky, Kz, Krotx, Kroty and Krotz, all set to zero.

Definition of the RBE3 constraint

bcRBE3=AFFE_CHAR_MECA(MODELE=CylModel,
                      LIAISON_RBE3=_F(GROUP_NO_MAIT='Nmaster',
                                      DDL_MAIT=('DX','DY','DZ','DRX','DRY','DRZ',),
                                      #DDL_MAIT=('DRZ',),
                                      GROUP_NO_ESCL='Nbot',
                                      DDL_ESCL='DX-DY-DZ',
                                      COEF_ESCL=1,),);

torsion=AFFE_CHAR_MECA(MODELE=CylModel,
                       FORCE_NODALE=_F(GROUP_NO='Nmaster', MZ=1000,),); 

RESU=MECA_STATIQUE(MODELE=CylModel,
                   CHAM_MATER=AssyMat,
                   CARA_ELEM=N_stmass,
                   EXCIT=(_F(CHARGE=bc,),
                          _F(CHARGE=bcRBE3),
                          _F(CHARGE=torsion),),);

The first AFFE_CHAR_MECA command defines the RBE3 constraint between the master node 'Nmaster' and the slave nodes 'Nbot'. The nodes 'Nbot' are attached to the geometrical entity GROUP_MA='Abot', by the DEFI_GROUP command. The second AFFE_CHAR_MACE command is used to apply the torsion moment MZ equal to 1000 (let us say [Nm], if we effectively say that all dimensions are in [m], forces are in [N] and pressures and Youngs' modulus are in [Pa]).

Results - displacements

File:Kw cylinder rbe3 displacement1.png

In the picture the rotation of the cylinder is nicely visible. It seems that the RBE3 function does what it is supposed to do: apply an external force without additional stiffness to the slave geometry.

to be continued