Thick cylinder prescribed normal expansion
StaticPASS · 0.24%Prescribed non-zero displacement along surface normal (d ≠ 0): thick cylinder expanded radially by d = 50 μm on outer surface, verified against Lamé analytical elasticity.
- Tolerance:
- 5%
Problem statement
- Geometry
- Hollow thick-walled cylinder: inner radius a = 50 mm, outer radius b = 100 mm, length L = 20 mm.
- Material
- Structural steel: E = 200 GPa, ν = 0.3.
- Boundary conditions
- Prescribed displacement along surface normal d = +50 μm on outer surface r = b; inner surface r = a free; axial plane strain (uz = 0) on both end faces.
- Measured quantity
- Inner surface radial displacement u_r(a). Analytical Lamé gives 53.85 μm; FEA computes 53.72 μm (deviation 0.24%). Outer surface matches prescribed displacement d = 50.00 μm to 0.000003%.
Results comparison
| Reference value | 53.85 um |
| Our result | 53.72 um |
| Deviation | 0.24% |
| Tolerance | 5% |
| Status | PASS · 0.24% |
| Element family | Solid element |
| Mesh details | 72×10×2 structured tetrahedral mesh (8640 tets, 1584 nodes) |
Updated: 2026-08-06 · WebCAE solver