2.1.2 Geometrically nonlinear analysis of a cantilever beam

Product: ABAQUS/Standard  

Most of the elements in ABAQUS are written for arbitrarily large displacements and rotations in geometrically nonlinear analysis. Such a capability is particularly important for slender (thin) structures, such as beams and shells. The two problems presented here illustrate the accuracy of several of the beam and continuum elements in large-displacement cases. The first problem is a cantilever loaded at its tip by a load of constant vertical direction. The second is the problem of a cantilever with a tip moment.

Problem description

Loading

For the transverse load case a total vertical load of 269.35 N is applied at the tip of the cantilever, which causes the tip to deflect more than 8 m.

For the moment load problem two different methods of applying the load to the beam tip are used. In the first a moment of 3384.78 N-m is applied to the end of the closed-section pipe beam and a moment of 2873.09 N-m is applied to the open-section I-beam. In the second method, which is most commonly used for prescribing rotations of more than radians, a constant angular velocity of 12.5664 rad/time is prescribed at the tip. Since the problem under consideration is a static analysis, ABAQUS interprets the angular velocity in terms of the normalized time used for incrementation. An amplitude reference is used to keep the angular velocity constant. The beam will wind around itself twice with either the applied moment or the prescribed angular velocity. Boundary conditions, Section 27.3.1 of the ABAQUS Analysis User's Manual, provides details of the method illustrated here to prescribe rotations of more than radians.

For the continuum elements the moment is applied through a distributing coupling constraint. The distributing coupling constraint is used to couple the nodes at the cantilever tip to a reference node placed at the tip. The moment is applied to this reference node resulting in a force-couple at the bottom and top nodes of the cantilever tip.

Results and discussion

Input files

References

Figures

Figure 2.1.2–1 Displacement plots for coarse mesh of cantilever beam with transverse loading.

Figure 2.1.2–2 Displacement plots for fine mesh of cantilever beam with transverse loading.

Figure 2.1.2–3 Displacement history of tip of coarse mesh of cantilever beam with transverse loading.

Figure 2.1.2–4 Displacement history of tip of fine mesh of cantilever beam with transverse loading.

Figure 2.1.2–5 Displacement plots of cantilever with moment loading.

Figure 2.1.2–6 Displacement plots of cantilever with moment loading.