Rigid body as an MPC

The final configuration for the problem is shown in Figure 2. The bottom plate moves with the top plate so that the final configuration is similar to the original configuration except for a unified rotation and translation. This is because the rigid body TIE NSET constrains both the displacements and the rotations of the nodes that belong to it.

The results obtained using rigid body node sets closely match those obtained from solving the corresponding MPC problem. From Figure 3, Figure 4, and Figure 5 it is clear that the leading characteristics of the solution—the $u_x$-displacement, the $u_z$-displacement, and the ${\theta }_x$-rotation—are almost identical for the problem solved with rigid bodies and the corresponding BEAMMPC problem. The differences observed in the ${\theta }_x$-rotation between Abaqus/Explicit and Abaqus/Standard are due to the different formulations used in the respective codes.