Twisted ribbon test for shells

This problem illustrates the use of shell elements for bending of a twisted plate. The results are compared with the reference solution by Batoz (1982).

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ProductsAbaqus/Standard

Problem description

The original problem description and the benchmark solutions can be found in Batoz (1982).

The length of the plate is varied from 2.0 to 10.0 to study aspect ratio effects. The material is linear elastic with a Young's modulus of 1 × 107 and a Poisson's ratio of 0.25. Nodes along edge A⁢D are clamped. The plate is twisted by applying a force of −1.0 at node B, and an equal and opposite force at node C. Gauss integration is used for the shell cross-section for the S9R5 element.

Results and discussion

The vertical displacement at node C is found as a function of the plate's aspect ratio. Since the plate's width is 1.0, the aspect ratio is equal to the length, L. Figure 2 plots vertical displacement at C versus the length of the plate. All elements give reasonable numerical predictions compared with the reference solution; see Batoz (1982).

References

  1. Batoz,  J. L., “An Explicit Formulation for an Efficient Triangular Plate Bending Element,” International Journal for Numerical Methods in Engineering, vol. 18, pp. 1077–1089, 1982.

Figures

Figure 1. Model of plate.

Figure 2. Comparison of results.