{
 "title": "Scordelis–Lo roof with one layer of hex20 reduced-integration solids",
 "kind": "benchmark",
 "source": "MacNeal and Harder, 'A proposed standard set of problems to test finite element accuracy', Finite Elements in Analysis and Design 1 (1985) 3–20: Fig. 8 (p. 8) geometry, material and load; Table 5(a) (p. 11) reference displacement 0.3024; Belytschko et al., Computer Methods in Applied Mechanics and Engineering 51 (1985) 221–258 (shell obstacle course)",
 "quantities": [
  {
   "id": "uz",
   "quantity": "vertical displacement at the midpoint of the free edge, mid-surface",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Load",
     "at": [
      [
       0,
       16.069690242163,
       19.151111077974
      ]
     ]
    },
    "pointer": "/nodes/0/displacement/2"
   },
   "value": -0.3024,
   "tolerance": {
    "relative": 0.02
   },
   "reason": "MacNeal and Harder grade an element A within 2% of the theoretical value on this prescribed coarse mesh (p. 14); MacNeal and Harder normalise by 0.3024 (the deep-shell value quoted in their [5] is 0.3086), and a solid model of R/t = 100 differs from shell theory by O(t/R)",
   "fixture_relative": 1e-7,
   "fixture_reason": "a thin shell (R/t = 100) of one layer of solids is ill-conditioned: rounding moves u_z by about 1e-9 relative between equivalent orderings of the arithmetic (8e-10 when the solver's factorisation changed in #50, 1e-10 from the interpolation order in #52, more between platforms); 1e-7 still catches any real change"
  }
 ]
}