NAFEMS T1
ThermomechanicalPASS · 0.65%Membrane with a circular hot spot — steady-state thermoelastic stress at the spot boundary; the target is independently reproducible by the circular-inclusion closed form sigma = E*alpha*dT/2.
- Tolerance:
- 5%
Problem statement
- Geometry
- Square membrane 20 mm x 20 mm, thickness 1 mm, with a central circular hot spot of radius 1 mm; a quarter (10 mm x 10 mm) is modeled with symmetry conditions; plane stress.
- Material
- E = 100 GPa, nu = 0.3; thermal strain alpha*dT = 1e-3 inside the hot spot (alpha = 1e-5 1/C, dT = 100 C), zero outside.
- Boundary conditions
- Quarter symmetry: uy = 0 along y = 0, ux = 0 along x = 0; outer edges free; no mechanical load — the loading is the thermal strain of the spot.
- Measured quantity
- Direct stress sigma_yy at point D = (1, 0) mm, just outside the spot boundary — reference value 50.0 MPa (closed form for a circular inclusion in an infinite plate: E*alpha*dT/2 = 50.0 MPa exactly).
Results comparison
| Reference value | 50.0 МПа (TNSB-1990аналитика включения E·αΔT/2 = 50.0 МПа точно) |
| Our result | 50.326 МПа (24×32), 50.299 МПа (16×24)внутри пятна -49.690 МПа |
| Deviation | 0.65% |
| Tolerance | 5% |
| Status | PASS · 0.65% |
| Element family | Shell element |
| Mesh details | четверть мембраны 10×10 мм, полярная сетка конформна границе пятна: SHELL_TRI веер в центре + MITC4 кольца (16×24 и 24×32 по θ×кольцам), геометрическое сгущение у r=1 мм; (мембранная ε_th у оболочек), αΔT=1e-3 внутри пятна; σθθ(D): 50.299 → 50.326 МПа, внутри пятна -49.690 МПа |
Updated: 2026-08-10 · WebCAE solver