Your tasks
- 4-node elements, 2 × 2 mesh: read the tip deflection. How far is it from beam theory?
Check answer
−0.1306 m, the text’s (3.49). Timoshenko beam theory gives −0.192 m (0.160 bending + 0.032 shear), so the hand mesh is 32% too stiff.
- Same eight elements, two layouts: 4-node 4 × 2 and 8 × 1. Then try 2 × 4. Which is stiffest, and why?
Check answer
4 × 2: −0.164 m; 8 × 1: −0.166 m; 2 × 4: −0.133 m. Elements that are long in the bending direction (a/b large) cannot bend without a spurious shear strain, so they lock. Element shape matters more than element count.
- Find the coarsest mesh within 2% of −0.192 m, first with 4-node and then with 8-node elements. Compare their degrees of freedom.
Check answer
4-node 16 × 8: −0.1886 m (−1.7%) with 306 dofs. 8-node 4 × 2: −0.1885 m (−1.8%) with 74 dofs. The quadratic element needs about a quarter of the unknowns because its edges can curve.
- Switch to plane strain on a fine mesh. What is the ratio of the two deflections, and why?
Check answer
About 0.90 (−0.171 against −0.191 m on 32 × 16). Plane strain stops the plate thinning, so the bending stiffness rises from E to E/(1 − ν²); 1 − ν² = 0.89.
More to try (the ANSYS demo’s wrong models)
- Load: point force at the top corner. The loaded corner deflects more than under the edge traction, and more with every refinement (4-node 8 × 4, 16 × 8, 32 × 16: −0.197, −0.210, −0.219 m against −0.182, −0.189, −0.191 m): a point force in 2D gives an infinite local displacement. Mid-span is unchanged.
- Support: vertical only. Nothing stops the plate sliding in x, and the solver refuses.
- Model data: thickness 1 m instead of 0.01 m. The deflection falls by exactly 100.
Element
Mesh (along × through the depth)
Idealisation
Load on the free end
Support on the left edge
Display
Model data
Mesh study
Both element types, five meshes each, with the current idealisation, load, support and model data.