{
 "title": "Thick-walled cylinder under internal pressure, 2D plane strain (Lamé)",
 "kind": "theory",
 "source": "Lamé's solution, Timoshenko and Goodier, Theory of Elasticity, 3rd ed., McGraw-Hill 1970, §28",
 "quantities": [
  {
   "id": "ur_a",
   "quantity": "radial displacement at the bore (10, 0)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Pressure",
     "at": [
      [
       10.0,
       0,
       0
      ]
     ]
    },
    "pointer": "/nodes/0/displacement/0"
   },
   "value": 0.00907936507936508,
   "tolerance": {
    "relative": 0.001
   },
   "reason": "quadratic elements on 8 radial divisions resolve u_r = A r + B/r to well under 0.1%"
  },
  {
   "id": "hoop_a",
   "quantity": "hoop stress σ_θ = σ_yy at the bore (10, 0)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Pressure",
     "at": [
      [
       10.0,
       0,
       0
      ]
     ]
    },
    "pointer": "/nodes/0/stress/1"
   },
   "value": 166.66666666666666,
   "tolerance": {
    "relative": 0.01
   },
   "reason": "stress extrapolated to the bore surface and averaged over two elements: about 0.5%"
  },
  {
   "id": "szz",
   "quantity": "axial stress σ_zz = 2νA at the bore (plane strain)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Pressure",
     "at": [
      [
       10.0,
       0,
       0
      ]
     ]
    },
    "pointer": "/nodes/0/stress/2"
   },
   "value": 20.0,
   "tolerance": {
    "relative": 0.01
   },
   "reason": "σ_zz = ν(σ_r + σ_θ) follows the in-plane stresses, extrapolated as they are"
  }
 ]
}