This problem demonstrates the use of the *CLOAD option with CPE4R, CPE6M, and C3D10M elements in a large-strain analysis. Two beams are analyzed together. Both beams are cantilevered on one end and are subjected to a force couple (a balanced set of loads on the translation degrees of freedom) on the other end. The couple on Beam 1 (the upper beam) is comprised of follower forces, so the applied moment is independent of tip rotation. Non-follower forces generate the moment on Beam 2 (the lower beam), so the moment is a function of the tip rotation.

This problem also demonstrates a technique for introducing follower forces into a mesh generated using solid elements. A follower force in ABAQUS requires a rotational degree of freedom to introduce change of direction of the application of the force. However, nodes attached to solid elements have only translational degrees of freedom. The BEAM MPC is used to activate rotational degrees of freedom at nodes where the forces are applied. The LINEAR MPC is used to constrain the end of the beam to remain a plane section.

Each beam is 400 mm long (L) and 20 mm thick (h). In the finite element model all the nodes at the right side are pinned, and the nodes at the left are constrained with BEAM and LINEAR MPCs so that they remain in a straight line of constant length.

The material for this problem is elastic with a constant Young's modulus of 1000 MPa and a Poisson's ratio of 0. The density is 10000 kg/m³.

For small-strain elasticity the moment per unit width required to form a beam into a circle is given by

The force required for this moment (using the beam thickness as the moment arm) is 523.6 × 10³ N. Because of dynamic effects the required forces are only 490.0 × 10³ N for the CPE4R mesh, 510.0 × 10³ N for the CPE6M mesh, and 4900.0 N for the C3D10M mesh. These forces are ramped on linearly over the analysis time of 0.2 seconds. The time period is chosen so that the quasi-static response can be observed with a minimum of dynamic vibration.