oracle: 2D cases (Kirsch plane stress, Lamé plane strain and axisymmetric, rotating disc and cylinder, NAFEMS LE1 with quad8) and J2 uniaxial explicit

The pending 2D LE1 case becomes a real one; the plasticity cases stay
pending with what they still need (static J2 for the collapse pressure,
the transcribed measurements for the Taylor bar).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed 2026-10-13 21:42:19 -04:00
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{
"title": "Rotating disc with a central hole, plane stress",
"kind": "theory",
"source": "Timoshenko and Goodier, Theory of Elasticity, 3rd ed., McGraw-Hill 1970, §32 (rotating disc of uniform thickness with a hole)",
"quantities": [
{
"id": "hoop_bore",
"quantity": "hoop stress σ_θ = σ_yy at the bore (20, 0)",
"measure": {
"command": "solve.probe",
"params": {
"step": "Spin",
"at": [
[
20.0,
0,
0
]
]
},
"pointer": "/nodes/0/stress/1"
},
"value": 65.312,
"tolerance": {
"relative": 0.01
},
"reason": "stress extrapolated to the bore surface, where the a²b²/r² term is steepest: 16 radial quadratic elements graded towards the bore leave about 0.2% (8 uniform: −2.4%; 32 graded: −0.05%)"
},
{
"id": "radial_max",
"quantity": "radial stress σ_r = σ_xx at r = √(ab), its maximum",
"measure": {
"command": "solve.probe",
"params": {
"step": "Spin",
"at": [
[
44.721359549995796,
0,
0
]
]
},
"pointer": "/nodes/0/stress/0"
},
"value": 20.724,
"tolerance": {
"relative": 0.01
},
"reason": "the nearest node to √(ab) is within half an element of it, where σ_r is stationary (an error of order (h/r)², under 0.5%), and nodal averaging adds a few tenths of a percent"
},
{
"id": "hoop_rim",
"quantity": "hoop stress σ_θ = σ_yy at the rim (100, 0)",
"measure": {
"command": "solve.probe",
"params": {
"step": "Spin",
"at": [
[
100.0,
0,
0
]
]
},
"pointer": "/nodes/0/stress/1"
},
"value": 16.328,
"tolerance": {
"relative": 0.01
},
"reason": "as at the bore"
}
]
}