engine: heated-bracket sample, steady heat and thermal stress in steel

file.sample heated-bracket: the corpus filleted bracket in steel, tet10, its
hole bores clamped, the upright's end held at 120 C and the rest cooled by
still air; one coupled temperature-displacement step. Its test checks the
temperatures against the heater and the air, then warms the bracket evenly,
clamps one hole, and matches the free thermal expansion alpha dT times the
distance from the hole along x.

Closes #165

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

docs/examples.md

@@ -67,3 +67,27 @@ Reynolds number and rises as it falls); the lattice's mass changes by less than
 
 There is no picture yet: the viewport does not draw flow results (velocity slices and
 streamlines are planned in M12), so this example is numbers only for now.
+
+## Heated bracket (`heated-bracket`)
+
+![The steel bracket's temperature, 120 °C at the heated end of the upright falling to 95 °C at the foot](media/examples/heated-bracket.png)
+
+The corpus filleted bracket (`tests/corpus/filleted-bracket`: an 8 mm L-bracket, R6 fillet, a
+hole through each leg) in steel, both hole bores clamped. The end of the upright is held at
+120 °C by a heater; the rest of its outside loses heat to still air at 20 °C
+(h = 10 W/(m² K)); steel conducts with k = 50 W/(m K), expands with α = 12 × 10⁻⁶/K and is
+stress free at 20 °C. One coupled temperature–displacement step (steady) on 23 641 tet10
+elements: about 8 s to open (meshing) and 13 s to solve.
+
+**Look at:** Contours ▸ Temperature: the upright stays within a few degrees of the heater and
+the foot falls to 95 °C, a steady balance between conduction and the air. Contours ▸ Von Mises
+shows the stress of the growth the clamps hold back: tens of MPa through the legs, peaking at the
+edges of the clamped bores, where a rigid clamp is a stress singularity (about 1 GPa there, a
+figure that grows as the mesh is refined: read the stress a little away from the bore).
+
+**Check:** the temperatures lie between the air's and the heater's and fall away from the heater.
+For the expansion, the test puts the air at the heater's temperature, so the bracket warms
+evenly by ΔT = 100 K, and clamps the foot's hole alone: the bracket then grows freely about it,
+and a point moves α ΔT times its distance from the hole's axis. The upright's top moves −0.0432
+mm along x (within 2 %); the foot's end, 16 mm from the clamped bore, which cannot grow, moves
+0.0228 mm against 0.024 mm (within 6 %).