Shell bending under a tip load

This example illustrates the use of shell elements to model a beam bending as a result of a tip load.

This page discusses:

ProductsAbaqus/StandardAbaqus/Explicit

Problem description

Two beams are analyzed in the same run, the first (BEAM1) with a follower load and the second (BEAM2) with a constant-direction load (a nonfollower load).

Each beam is 400 mm long in the x-direction, with a 20-mm-square cross-section. There are 40 elements along the length. Thus, each beam has 40 S4R elements and 82 nodes. All nodes are constrained in degrees of freedom 3–5, and the ends of both beams are constrained in degrees of freedom 1–6.

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.

Both beams are loaded with a general edge traction of 12500 N/m in the negative y-direction at each end node. The load on the first beam is a follower force, while the load on the second beam does not change direction as the beam deforms.

Results and discussion

Figure 1 displays the Abaqus/Explicit contours of the axial membrane section force, SF1, for both beams loaded by the distributed force. In Beam 1 the section force is zero at the tip, increasing to maximum compression at the base. In Beam 2 the section force is zero at the base, increasing to maximum tension at the tip. Figure 2 shows a time history of the tip deflection of both beams.

The predicted vertical steady-state displacement at the tip of the first beam (with a follower load) compares well with the Abaqus/Standard result of 291 mm.

The predicted vertical steady-state displacement at the tip of the second beam (with a constant-direction load) compares well with the analytical result of 240 mm given by Bisshopp and Drucker (1945) and the Abaqus/Standard result of 242 mm.

Input files

shellfoll_xpl_edld.inp

Abaqus/Explicit analysis of two beams, one with a follower edge traction and the other with a nonfollower edge traction.

shellfoll_std_edld.inp

Abaqus/Standard analysis of two beams, one with a follower edge traction and the other with a nonfollower edge traction.

References

  1. Bisshopp,  K. E.,  and D. C. Drucker, “Large Deflections of Cantilever Beams,” Quarterly of Applied Mathematics, vol. 3 272, 1945.

Figures

Figure 1. Contours of axial section force.

Figure 2. Tip deflection history.