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oracle: filleted L-bracket on the octree all-hex mesh
A slow theory case: the corpus bracket meshed by mesh.hex.octree at 7, 5 and 4 mm, clamped at the base and loaded by 2 kN. Checks equilibrium, that every element is certified valid, the mesh volume against the CAD volume, the beam bending stress of the upright leg (sigma = M c / I = 145.3 MPa, within 5%) and the convergence of the fillet von Mises stress against the 4 mm mesh. Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed
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# Filleted L-bracket on the octree all-hex mesh
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The corpus part `filleted-bracket` (an 8 mm thick L, 60 × 50 × 40 mm, an R6 fillet inside the
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corner and a Ø8 hole through each leg), built with SolidCraft from `design.json` and meshed by
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`mesh.hex.octree` (hex8 with incompatible modes, steel E = 210 GPa, ν = 0.3). The bottom face of
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the horizontal leg (`F2:side:l1`) is clamped and the top face of the upright leg (`F2:side:l5`)
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carries 2 kN along +x.
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Checked on the 5 mm mesh: equilibrium; the certified validity of every element; the mesh volume
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against the CAD volume; the bending stress of the upright leg at y = 19 on both faces,
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σ_yy = M c / I = 2000 · 31 · 4 / 1706.7 = 145.3 MPa (M is exact by statics, the plane-section
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stress is the reference, the corner and a hole are near). The von Mises stress at the middle of
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the fillet, which has no closed form, is checked for convergence against the 4 mm mesh:
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| mesh size | hexahedra | fillet von Mises (MPa) | σ_yy outer / inner at y = 19 (MPa) |
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|---|---|---|---|
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| 7 mm | 4291 | 138.5 | 149.4 / −146.9 |
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| 5 mm | 13273 | 144.5 | 149.3 / −147.3 |
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| 4 mm (reference) | 21508 | 143.2 | 147.4 / −145.5 |
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A 3 mm mesh needs more than the direct solver's factor cap.
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@@ -0,0 +1,89 @@
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{
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"commands": [
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{
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"command": "sketch.create",
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"params": {
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"plane": "XY",
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"name": "Profile"
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}
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},
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{
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"command": "sketch.line",
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"params": {
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"points": [
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[
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0,
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0
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],
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[
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60,
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0
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],
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[
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60,
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8
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],
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[
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8,
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8
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],
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[
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8,
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50
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],
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[
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0,
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50
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]
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],
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"closed": true
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}
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},
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{
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"command": "sketch.finish",
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"params": {}
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},
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{
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"command": "solid.extrude",
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"params": {
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"distance": 40,
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"body_name": "Bracket"
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}
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},
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{
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"command": "solid.fillet",
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"params": {
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"edges": [
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[
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8,
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8,
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20
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]
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],
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"radius": 6
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}
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},
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{
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"command": "solid.hole",
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"params": {
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"position": [
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40,
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8,
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20
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],
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"diameter": 8
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}
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},
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{
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"command": "solid.hole",
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"params": {
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"position": [
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8,
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32,
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20
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],
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"diameter": 8
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}
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}
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]
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}
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@@ -0,0 +1,99 @@
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{
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"title": "Filleted L-bracket on the octree all-hex mesh: equilibrium, beam bending, fillet stress convergence",
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"kind": "theory",
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"source": "equilibrium; Euler–Bernoulli bending of the 8 × 40 mm leg, σ = M c / I with M = F (50 − y) (S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd ed., 1970, §102); grid convergence of the fillet stress against the 4 mm mesh of this case (P. J. Roache, Verification and Validation in Computational Science and Engineering, 1998, ch. 5)",
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"slow": true,
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"quantities": [
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{
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"id": "reaction_x",
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"quantity": "x reaction on the clamped face (5 mm mesh)",
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"measure": {
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"from": "solve5",
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"pointer": "/reaction_total/0"
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},
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"value": -2000.0,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "the reactions balance the 2 kN load to solver precision"
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},
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{
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"id": "invalid",
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"quantity": "elements the certified Jacobian check does not prove valid (5 mm mesh)",
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"measure": {
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"from": "quality5",
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"pointer": "/invalid/count"
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},
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"value": 0.0,
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"tolerance": {
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"exact": true
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},
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"reason": "the octree mesher returns only elements proven valid"
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},
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{
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"id": "volume",
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"quantity": "mesh volume against the CAD volume (5 mm mesh)",
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"measure": {
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"from": "mesh5",
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"pointer": "/bodies/0/volume"
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},
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"value": 32144.778925,
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"tolerance": {
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"relative": 0.003
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},
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"reason": "bilinear boundary faces on the R6 fillet and the two Ø8 holes, and the 1e-3 chordal tessellation they are fitted to"
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},
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{
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"id": "syy_outer",
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"quantity": "σ_yy on the outer face of the upright leg at y = 19, z = 6 (5 mm mesh)",
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"measure": {
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"from": "probe5",
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"pointer": "/nodes/1/stress/1"
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},
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"value": 145.3125,
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"tolerance": {
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"relative": 0.05
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},
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"reason": "beam theory ignores the corner 5 mm below and the hole 9 mm above; the probe takes the nearest node's extrapolated stress"
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},
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{
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"id": "syy_inner",
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"quantity": "σ_yy on the inner face of the upright leg at y = 19, z = 6 (5 mm mesh)",
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"measure": {
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"from": "probe5",
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"pointer": "/nodes/2/stress/1"
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},
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"value": -145.3125,
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"tolerance": {
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"relative": 0.05
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},
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"reason": "as for the outer face"
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},
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{
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"id": "fillet_7",
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"quantity": "von Mises stress at the middle of the fillet, 7 mm mesh",
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"measure": {
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"from": "probe7",
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"pointer": "/nodes/0/von_mises"
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},
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"value": 143.21,
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"tolerance": {
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"relative": 0.05
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},
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"reason": "the coarsest mesh, within 5% of the 4 mm mesh"
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},
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{
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"id": "fillet_5",
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"quantity": "von Mises stress at the middle of the fillet, 5 mm mesh",
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"measure": {
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"from": "probe5",
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"pointer": "/nodes/0/von_mises"
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},
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"value": 143.21,
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"tolerance": {
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"relative": 0.02
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},
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"reason": "converging: within 2% of the 4 mm mesh"
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}
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]
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}
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@@ -0,0 +1,33 @@
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{
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"note": "FieldCraft's accepted results for this case, written by `cargo xtask oracle --bless`. A result outside its band fails CI.",
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"values": {
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"fillet_5": {
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"band": 1.4452906175564113e-7,
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"value": 144.52906175564112
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},
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"fillet_7": {
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"band": 1.4321000000000002e-7,
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"value": 138.5286423070889
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},
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"invalid": {
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"band": 0.0,
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"value": 0.0
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},
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"reaction_x": {
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"band": 2.0000000000000003e-6,
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"value": -1999.999999998785
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},
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"syy_inner": {
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"band": 1.472793063397077e-7,
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"value": -147.2793063397077
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},
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"syy_outer": {
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"band": 1.4926027331710374e-7,
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"value": 149.26027331710372
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},
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"volume": {
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"band": 0.00003217691091849411,
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"value": 32176.910918494108
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}
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}
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}
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@@ -0,0 +1,228 @@
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[
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{
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"command": "model.material.create",
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"params": {
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"name": "Steel",
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"elastic": {
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"type": "isotropic",
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"young": 210000.0,
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"poisson": 0.3
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}
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}
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},
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{
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"command": "mesh.hex.octree",
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"params": {
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"body": "Bracket",
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"size": 7.0
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},
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"id": "mesh7"
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},
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{
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"command": "model.set.create",
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"params": {
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"name": "all",
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"geometry": [
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{
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"body": "Bracket"
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}
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]
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}
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},
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{
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"command": "model.set.create",
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"params": {
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"name": "base",
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"geometry": [
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{
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"body": "Bracket",
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"face": "F2:side:l1"
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}
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]
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}
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},
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{
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"command": "model.set.create",
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"params": {
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"name": "top",
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"geometry": [
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{
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"body": "Bracket",
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"face": "F2:side:l5"
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}
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]
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}
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},
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{
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"command": "model.section.create",
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"params": {
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"name": "solid",
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"set": "all",
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"material": "Steel",
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"kind": {
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"type": "solid"
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},
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"formulation": {
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"incompatible_modes": true
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}
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}
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},
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{
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"command": "model.boundary_condition.create",
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"params": {
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"name": "clamp",
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"type": "fixed",
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"target": {
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"set": "base"
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}
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}
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},
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{
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"command": "model.load.create",
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"params": {
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"name": "F",
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"type": "force",
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"target": {
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"set": "top"
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},
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"vector": [
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2000.0,
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0,
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0
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]
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}
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},
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{
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"command": "model.step.create",
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"params": {
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"name": "Load",
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"procedure": {
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"type": "static"
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},
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"boundary_conditions": [
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"clamp"
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],
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"loads": [
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"F"
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]
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}
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},
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{
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"command": "mesh.quality",
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"params": {},
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"id": "quality7"
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},
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{
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"command": "solve.static",
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"params": {},
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"id": "solve7"
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},
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{
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"command": "solve.probe",
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"params": {
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"step": "Load",
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"at": [
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[
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9.757359312880714,
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9.757359312880714,
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10.0
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],
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[
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0.0,
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19.0,
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6.0
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],
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[
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8.0,
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19.0,
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6.0
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]
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]
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},
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"id": "probe7"
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},
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{
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"command": "mesh.hex.octree",
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"params": {
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"body": "Bracket",
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"size": 5.0
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},
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"id": "mesh5"
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},
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{
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"command": "mesh.quality",
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"params": {},
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"id": "quality5"
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},
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{
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"command": "solve.static",
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"params": {},
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"id": "solve5"
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},
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{
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"command": "solve.probe",
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"params": {
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"step": "Load",
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"at": [
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[
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9.757359312880714,
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9.757359312880714,
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10.0
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],
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[
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0.0,
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19.0,
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6.0
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],
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[
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8.0,
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19.0,
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6.0
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]
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]
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},
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"id": "probe5"
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},
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{
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"command": "mesh.hex.octree",
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"params": {
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"body": "Bracket",
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"size": 4.0
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},
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"id": "mesh4"
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},
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{
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"command": "mesh.quality",
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"params": {},
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"id": "quality4"
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},
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{
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"command": "solve.static",
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"params": {},
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"id": "solve4"
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},
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{
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"command": "solve.probe",
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"params": {
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"step": "Load",
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"at": [
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[
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9.757359312880714,
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9.757359312880714,
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10.0
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],
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[
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0.0,
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19.0,
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6.0
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],
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[
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8.0,
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19.0,
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6.0
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]
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]
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},
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"id": "probe4"
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}
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]
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Block a user