Hybrid mesh: hex-layer zone on a hole wall, stress concentration of a finite-width plate
Meshing / hybrid hex + tet zonesPASS · 2.3%A plate with a central hole under uniform tension. A layer of structured elements (4 wedge layers, graded towards the wall) is built on the hole surface (refine tube), the rest of the body is tetrahedra; the layer is welded to the tet mesh through shared nodes. The peak stress at the hole edge is compared with the Peterson/Howland finite-width correction of the Kirsch solution.A plate with a central hole under uniform tension. A layer of structured elements (4 wedge layers, graded towards the wall) is built on the hole surface (refine tube), the rest of the body is tetrahedra; the layer is welded to the tet mesh through shared nodes… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Quarter of a plate 240 × 60 × 4 mm (full width W = 120 mm) with a hole of radius 5 mm at the origin (d/W = 0.0833). Hex zone: tube on the hole surface, thickness 3 mm, 4 layers, bias 1.3, weld.
- Material
- Steel: E = 200 GPa, ν = 0.3.
- Boundary conditions
- Symmetry planes x = 0 and y = 0 (normal displacement fixed), both z faces fixed in z (plane strain), uniform tension 100 MPa on the far end.
- Measured quantity
- Maximum nodal principal stress σ1,max (the hoop stress at the hole edge) against Kt,net · σ·W/(W − d), Kt,net = 3.0 − 3.13λ + 3.66λ² − 1.53λ³, λ = d/W.
WebCAE Terminal
Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:
units mm
material E=2e11 nu=0.3
primitive box dx=240 dy=60 dz=4
primitive cylinder r=5 h=4
boolean cut target=body1 tool=body2
list faces of body3
refine tube surface=35 thickness=3 layers=4 bias=1.3 size=0.8
mesh tet size=12
fix surface number 1 component=x
fix surface number 3 component=y
fix surface number 5 component=z
fix surface number 6 component=z
load surface number 2 pressure=-1e8
solve
minmax principalMaxResults comparison
| Reference value | σ1,max = 301.5 МПа (Peterson/Howland: Kt,нетто = 2.764, d/W = 0.0833, σ_ном,нетто = 109.1 МПа) |
| Our result | σ1,max = 308.4 МПа (+2.30 %) |
| Deviation | 2.3% |
| Tolerance | 5% |
| Status | PASS · 2.3% |
| Mesh details | гибрид: тет4 1717 + призм wedge6 360 (слой 4 × t=3 мм, прогрессия 1.3 у стенки), 830 узлов (2490 ), глобальный размер 12 мм; расчёт native, скрипт 1.6 с |
Updated: 2026-10-22 · WebCAE solver