Problem. The cantilever bending in its own plane from the quadrilateral section is solved on a triangular mesh. In the triangle the rotation about the node normal is carried by Allman interpolation.
Reference document. The closed form of beam theory is used, the one that gives the bending and shear displacements together.
The horizontal tip displacement of the cantilever is the sum of the bending and shear contributions.
Numerical model. The cantilever is meshed with triangular shell elements and the out-of-plane freedoms are closed at every node. At the fixed end the in-plane translations and the rotation about the node are held.
Cantilever bending in its own plane, triangular mesh
Parameters. L/h = 10 · mesh = 20×4×2 triangles
Published source. Beam theory, bending and shear together
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| Horizontal tip displacement, bending and shear together | -0.134293 | -0.123307 | 8.18% |
Note. In this test the triangular mesh deviates by 8%. On the same problem the quadrilateral mesh stays within 0.5%. The difference comes from the known limit of the triangular element in in-plane bending.