RBE2 vs RBE3

Two common types of Rigid Body Elements (RBEs) are the RBE2 and RBE3. Multi point constraint MPC elements and can be included, or not, in the case control portion of the Bulk Data File (BDF). Both RBE2s and RBE3s are often used to connect one node to one or several nodes. This can be done for many reasons, for example to impart loads onto a model or to enforce a rigid connection between two nodes. RBE2 formulation consists of one independent node and one or more dependent node(s).
This is shown below in a FEMAP screenshot of the RBE2 formulation. It is important to note that on the dependent nodes the modeler may select DOF (degrees of freedom) TX - translation in the X direction, TY - translation in the Y direction, TZ - translation in the Z direction, RX - rotation about the X axis, RY - rotation about the Y axis, and RZ - rotation about the Z axis. These DOFs apply to all of the dependent nodes chosen.

RBE2 FEMAP formulation / setup

The RBE3 is similar in that it connects one node to one or more node(s) however it allows one dependent and one or more independent node(s). The DOFs are selectable on both the dependent and independent node sides. Independent nodes can have separate DOFs selected; this is different than the RBE2 Element formulation where only one set of DOFs is applied to all dependent nodes. In addition the node by node DOF selection, it is also possible to weight nodes effectivity which can be useful if a more specific node based distribution (rather than geometric) is required.

RBE3 FEMAP formulation / setup




One of the most common uses for the RBE3 is to "smear" a load into a structure. The RBE2 impose stiffness and are often called "infinitely stiff", while the RBE3 is an interpolation element and does not impart additional stiffness to the model.

To help illustrate this difference between the RBE2 and the RBE3 consider the following simple shelf model. The model is a two bay shelf and a vertical load is to be imparted in the center area of each bay.

Finite Element Shelf




The left side bay of the shelf is modeled and loads are imparted with an RBE2 while the right side uses an RBE3. The "footprint" of each multi point constraint is identically shaped and positioned in its bay.

FEA Shelf with load area highlighted

FEM shelf with with rigid body elements RBE2 & RBE3

The back edge of the shelf and the back vertical leg of the supports are fixed while at the single node in each RBE a vertical force is applied.

The following figure shows displacement after the analysis is completed. Notice how the left side bay was "reinforced" from the added stiffness of the RBE2, while the right side was not.


FEA shelf displacement plot


This effect is also apparent by investigating the stresses in the elements, as shown below:


FEA shelf stress plot (von mises) shownig difference between RBE2 & RBE3 footprint


It can be clearly seen the footprint under the RBE2 is stiffened by the formulation of the RBE2. Neither application, RBE2 or RBE3, is right or wrong; it simply depends on what the intent of the analysis is.  Take for example the RBE2, on the left, if the down force is due to an inertial load of a box on the shelf an RBE2 is appropriate assuming the box is stiff relative to the shelf. The RBE3 however is more like a deformable body loading the shelf bay.