verification: activate the two shell benchmark cases (#106)

The Scordelis-Lo roof and the pinched cylinder had their published
references cited but no recipe, because mesh.block's 2D form is planar
and cannot build a curved patch. Both are now active: the mesh is
written node by node (mesh.node.add / mesh.element.add, the route
docs/verification.md allows), the same cylinder patch the solver's own
benchmarks.rs builds in code, with the quarter/eighth symmetry planes,
the rigid diaphragm and the published load.

- scordelis-lo-roof-shell: 16x16 flat quad4 (MITC4) shells, R = 25,
  t = 0.25, self-weight 90 per area; u_z at the free-edge mid-span
  -0.3024 within 2% (ours -0.29901009815961804, 1.12% low).
- pinched-cylinder: 32x32 flat quad4 shells, R = 300, t = 3, a quarter
  of the unit pinch; u under the load -1.8248e-5 within 2% (ours
  -1.803845342860719e-05, 1.15% low).

Each README carries the generator (so the recipe is reproducible), the
refinement study the tolerance reason cites, and how the reference was
cited before. pinched-hemisphere and mh-twisted-beam now say what they
actually wait for: a doubly curved or helical shell mesh written node
by node, not missing shell elements.

docs/oracle.md

@@ -2,7 +2,7 @@
 
 Generated by `cargo xtask oracle` from [`tests/oracle/`](../tests/oracle/); the policy is [verification.md](verification.md). Every case is our own model, built with FieldCraft commands from the problem's published description, and compared with the reference value its `expected.json` cites, within the stated tolerance and for the stated reason. Accepted results are frozen in each case's `fixture.json`: a later change that moves one beyond its band (10⁻⁹ of its size) fails CI even while the reference still passes. No reference value was produced with a commercial product.
 
-**275 of 281 quantities pass** (6 known failure(s)) in 71 active cases: 62 theory, 9 published benchmark, 0 experiment; 10 pending cases wait for capabilities still being built.
+**277 of 283 quantities pass** (6 known failure(s)) in 73 active cases: 62 theory, 11 published benchmark, 0 experiment; 8 pending cases wait for capabilities still being built.
 
 ## Theory: closed-form solutions, patch tests and mesh invariants
 
@@ -293,6 +293,8 @@ Generated by `cargo xtask oracle` from [`tests/oracle/`](../tests/oracle/); the
 | [nafems-le1](../tests/oracle/nafems-le1/) | σ_yy at D (2, 0) | 92.7 | 92.869 | 0.182% | 1% | pass | matches |
 | [nafems-le1-plane-stress](../tests/oracle/nafems-le1-plane-stress/) | σ_yy at D (2, 0) | 92.7 | 92.648 | -0.0559% | 1% | pass | matches |
 | [nafems-le10](../tests/oracle/nafems-le10/) | σ_yy at D (2, 0, 0.3) on the loaded face | -5.38 | -5.3339 | 0.857% | 2% | pass | matches |
+| [pinched-cylinder](../tests/oracle/pinched-cylinder/) | radial displacement under the load, mid-surface | -1.8248e-5 | -1.8038e-5 | 1.15% | 2% | pass | matches |
+| [scordelis-lo-roof-shell](../tests/oracle/scordelis-lo-roof-shell/) | vertical displacement at the midpoint of the free edge, mid-surface | -0.3024 | -0.29901 | 1.12% | 2% | pass | matches |
 | [scordelis-lo-roof-solid](../tests/oracle/scordelis-lo-roof-solid/) | vertical displacement at the midpoint of the free edge, mid-surface | -0.3024 | -0.3014 | 0.33% | 2% | pass | matches |
 
 ## Sources and tolerances
@@ -359,11 +361,13 @@ Generated by `cargo xtask oracle` from [`tests/oracle/`](../tests/oracle/); the
 - **[patch-tet10](../tests/oracle/patch-tet10/)** (theory): Constant-stress patch test, tet10. Source: Irons and Razzaque, 'Experience with the patch test for convergence of finite elements', in Aziz (ed.), The Mathematical Foundations of the Finite Element Method, Academic Press 1972, pp. 557–587; MacNeal and Harder, Finite Elements in Analysis and Design 1 (1985) 3–20, constant-stress loading, p. 14 Table 7. Tolerances — ux: a patch test is passed exactly: the tolerance only admits rounding; uy: a patch test is passed exactly: the tolerance only admits rounding; uz: a patch test is passed exactly: the tolerance only admits rounding; sxx: a patch test is passed exactly: the tolerance only admits rounding; syy: a patch test is passed exactly: the tolerance only admits rounding; szz: a patch test is passed exactly: the tolerance only admits rounding; sxy: a patch test is passed exactly: the tolerance only admits rounding (stresses of order 1)
 - **[patch-tet4](../tests/oracle/patch-tet4/)** (theory): Constant-stress patch test, tet4. Source: Irons and Razzaque, 'Experience with the patch test for convergence of finite elements', in Aziz (ed.), The Mathematical Foundations of the Finite Element Method, Academic Press 1972, pp. 557–587; MacNeal and Harder, Finite Elements in Analysis and Design 1 (1985) 3–20, constant-stress loading, p. 14 Table 7. Tolerances — ux: a patch test is passed exactly: the tolerance only admits rounding; uy: a patch test is passed exactly: the tolerance only admits rounding; uz: a patch test is passed exactly: the tolerance only admits rounding; sxx: a patch test is passed exactly: the tolerance only admits rounding; syy: a patch test is passed exactly: the tolerance only admits rounding; szz: a patch test is passed exactly: the tolerance only admits rounding; sxy: a patch test is passed exactly: the tolerance only admits rounding (stresses of order 1)
 - **[patch-wedge6](../tests/oracle/patch-wedge6/)** (theory): Constant-stress patch test, wedge6. Source: Irons and Razzaque, 'Experience with the patch test for convergence of finite elements', in Aziz (ed.), The Mathematical Foundations of the Finite Element Method, Academic Press 1972, pp. 557–587; MacNeal and Harder, Finite Elements in Analysis and Design 1 (1985) 3–20, constant-stress loading, p. 14 Table 7. Tolerances — ux: a patch test is passed exactly: the tolerance only admits rounding; uy: a patch test is passed exactly: the tolerance only admits rounding; uz: a patch test is passed exactly: the tolerance only admits rounding; sxx: a patch test is passed exactly: the tolerance only admits rounding; syy: a patch test is passed exactly: the tolerance only admits rounding; szz: a patch test is passed exactly: the tolerance only admits rounding; sxy: a patch test is passed exactly: the tolerance only admits rounding (stresses of order 1)
+- **[pinched-cylinder](../tests/oracle/pinched-cylinder/)** (benchmark): Pinched cylinder with rigid diaphragms. Source: Belytschko, Stolarski, Liu, Carpenter and Ong, 'Stress projection for membrane and shear locking in shell finite elements', Computer Methods in Applied Mechanics and Engineering 51 (1985) 221–258 (the shell obstacle course); reference 1.8248 × 10⁻⁵ under the load. Tolerances — u: a fixed-mesh comparison at the conventional 32 × 32 eighth mesh, the mesh the solver's own in-code benchmark uses: the reference is the thin-shell value Belytschko et al. quote to four figures (1.8248 × 10⁻⁵), while the deflection under a point load has no mesh-converged limit in a Reissner–Mindlin (MITC4) shell, whose transverse shear force is unbounded at the load, so the value keeps rising with refinement (8 × 8, 16 × 16, 24 × 24, 32 × 32, 48 × 48 and 64 × 64 give 1.3559, 1.6942, 1.7735, 1.8038, 1.8275 and 1.8369 × 10⁻⁵, crossing the reference between 32 × 32 and 48 × 48 and staying above it); 2% is the margin the in-code benchmark gates 32 × 32 with, applied here to the same mesh (crates/solver/tests/benchmarks.rs, README)
 - **[plastic-hinge-cantilever](../tests/oracle/plastic-hinge-cantilever/)** (theory): Plastic collapse of a cantilever: the fully plastic moment at the root. Source: Limit analysis (B. G. Neal, The Plastic Methods of Structural Analysis, 3rd ed., Chapman & Hall 1977, ch. 1–2): beam theory's plastic hinge at the root, the fully plastic moment M_p = σ_y b h²/4 of a rectangular section, collapses a cantilever of length L at P_c = M_p/L = 312.5 (b = h = 10, L = 200, σ_y = 250); a bound for the solid, whose collapse lies above it (W. Prager, P. G. Hodge, Theory of Perfectly Plastic Solids, Wiley 1951: a continuum mechanism allows no normal velocity jump, which the beam's hinge rotation is). Tolerances — collapse_force: the solid's collapse lies above beam theory's hinge: refined through the depth (4 to 8 elements) and along the length (40 to 160) the force settles 3.1 % above M_p/L (322.3), so the band is that bound's gap; the root is a symmetry plane (no rotation, free lateral contraction) held on average through a coupling, the tip pushed through another; reduced hex20, 20 × 2 × 4
 - **[plastic-thick-cylinder](../tests/oracle/plastic-thick-cylinder/)** (theory): Elastic–perfectly plastic thick cylinder: plastic zone and collapse pressure. Source: Hill, The Mathematical Theory of Plasticity, Oxford 1950, ch. V §2: a von Mises cylinder in plane strain, elastically incompressible, with the plastic zone a ≤ r ≤ c under the pressure p = k (2 ln(c/a) + 1 − c²/b²), k = σ_y/√3, and the bore displacement u_a = k c²/(2 G a); collapse when c = b at p = 2k ln(b/a). Tolerances — u_bore: 20 reduced quad8 elements through the wall resolve the logarithmic plastic field and ν = 0.4999 stands in for Hill's incompressible elasticity (0.009 % apart); u_a ∝ c², so 0.2 % on u_a is 0.1 % on the plastic radius; collapse_force: once the wall is plastic through, perfect plasticity holds the force at the collapse value (σ_θ − σ_r = 2k everywhere, σ_z the mean of the others as plastic flow dominates); the band admits the quadrature of the logarithmic field
 - **[pure-bending-coupling](../tests/oracle/pure-bending-coupling/)** (theory): Pure bending through a distributing coupling. Source: Euler–Bernoulli pure bending, σ = M_y z/I, θ = ML/(EI) (exact in elasticity for ν = 0); Timoshenko and Goodier, Theory of Elasticity, 3rd ed., 1970, §102. Tolerances — sigma_top: with ν = 0 pure bending is a quadratic displacement field that hex20 represents exactly; the coupling's nodal force pattern differs from the linear traction only within a depth or two of the end (Saint-Venant), five depths from the probe; rotation: the reference point follows the best-fit rigid motion of the end section, which the end zone's local deformation disturbs by well under 1%
 - **[rotating-cylinder-axisymmetric](../tests/oracle/rotating-cylinder-axisymmetric/)** (theory): Long rotating solid cylinder, axisymmetric. Source: Timoshenko and Goodier, Theory of Elasticity, 3rd ed., McGraw-Hill 1970, §32 (long rotating cylinder, ε_z = 0). Tolerances — radial_axis: stress extrapolated to the axis, where σ_r = σ_θ: under 1% with sixteen quadratic elements across; hoop_rim: stress extrapolated to the surface: under 1%
 - **[rotating-disc-plane-stress](../tests/oracle/rotating-disc-plane-stress/)** (theory): Rotating disc with a central hole, plane stress. Source: Timoshenko and Goodier, Theory of Elasticity, 3rd ed., McGraw-Hill 1970, §32 (rotating disc of uniform thickness with a hole). Tolerances — hoop_bore: 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%); radial_max: 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; hoop_rim: as at the bore
+- **[scordelis-lo-roof-shell](../tests/oracle/scordelis-lo-roof-shell/)** (benchmark): Scordelis–Lo roof with shell elements. 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), Table 5(a) (p. 11); Belytschko, Stolarski, Liu, Carpenter and Ong, 'Stress projection for membrane and shear locking in shell finite elements', Computer Methods in Applied Mechanics and Engineering 51 (1985) 221–258 (the shell obstacle course). Tolerances — uz: MacNeal and Harder grade a thin-shell element within 2% of the theoretical value on a prescribed coarse mesh, the grading the sibling case scordelis-lo-roof-solid records (p. 14); this case uses 16 × 16, the mesh the solver's in-code gate test uses, and the flat MITC4 shell converges from below to the reference: 4 × 4, 8 × 8, 16 × 16, 32 × 32, 64 × 64 and 128 × 128 give 0.28459, 0.29401, 0.29901, 0.30060, 0.30118 and 0.30143, so 16 × 16 is 1.12% low and the mesh error shrinks monotonically inside the tolerance (README)
 - **[scordelis-lo-roof-solid](../tests/oracle/scordelis-lo-roof-solid/)** (benchmark): Scordelis–Lo roof with one layer of hex20 reduced-integration solids. 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). Tolerances — uz: 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)
 - **[tie-heat-series](../tests/oracle/tie-heat-series/)** (theory): Heat through a tie: two blocks of conductivities 10 and 40 with non-matching meshes, 20 and 100 at the ends. Source: Series thermal resistances: steady one-dimensional conduction through two layers in perfect contact, T_i = (k1 T0 + k2 T1)/(k1 + k2) and q = ΔT/(L1/k1 + L2/k2) (F. P. Incropera, D. P. DeWitt, Fundamentals of Heat and Mass Transfer, §3.1, the composite wall). A linear field in each layer is the exact discrete solution, and the dual mortar tie reproduces a linear temperature across non-matching meshes. Tolerances — t_interface: exact discrete solution: linear in each block, and the tie holds the interface temperature for non-matching meshes; t_lower: exact discrete solution: linear in each block, and the tie holds the interface temperature for non-matching meshes; t_upper: exact discrete solution: linear in each block, and the tie holds the interface temperature for non-matching meshes; q_lower: the heat flow ΔT/(1/k1 + 1/k2) = 640 per unit area, −k ∂T/∂z uniform in each block; q_upper: the same heat flow crosses the tie: nothing is lost at the interface
 - **[tie-patch](../tests/oracle/tie-patch/)** (theory): Tie patch test: two blocks with non-matching meshes tied together in uniaxial tension. Source: The patch test for mesh tying: a tie across non-matching meshes must transmit a constant stress exactly; B. I. Wohlmuth, A mortar finite element method using dual spaces for the Lagrange multiplier, SIAM J. Numer. Anal. 38(3):989–1012, 2000; M. A. Puso, A 3D mortar method for solid mechanics, IJNME 59:315–336, 2004. Uniaxial stress between frictionless symmetry planes is uniform in both blocks. Tolerances — szz_10: uniaxial stress E ε = 1000 × 0.01 is the exact discrete solution: the dual mortar conditions hold for the linear field on both meshes; szz_14: uniaxial stress E ε = 1000 × 0.01 is the exact discrete solution: the dual mortar conditions hold for the linear field on both meshes; szz_1: uniaxial stress E ε = 1000 × 0.01 is the exact discrete solution: the dual mortar conditions hold for the linear field on both meshes; szz_19: uniaxial stress E ε = 1000 × 0.01 is the exact discrete solution: the dual mortar conditions hold for the linear field on both meshes; szz_26: uniaxial stress E ε = 1000 × 0.01 is the exact discrete solution: the dual mortar conditions hold for the linear field on both meshes; sxx_14: the tie must not hold the lateral contraction of either mesh; uz_interface: the tied node follows the uniform strain field
@@ -378,10 +382,8 @@ Reference values already cited; each case gets its recipe when the capability it
 | [cylinder-channel-2d1](../tests/oracle/cylinder-channel-2d1/) | benchmark | Flow around a cylinder, steady 2D-1 (Re = 20) | lattice Boltzmann CFD (M12) | drag coefficient (published interval 5.57–5.59) = 5.58; lift coefficient (interval 0.0104–0.0110) = 0.0107 | Schäfer and Turek, 'Benchmark computations of laminar flow around a cylinder', Notes on Numerical Fluid Mechanics 52 (1996) 547–566, Table 4 (reference intervals) |
 | [explicit-hertz-spheres](../tests/oracle/explicit-hertz-spheres/) | theory | Two elastic spheres in a head-on collision: Hertz's force and contact duration (explicit contact) | a graded sphere mesh from commands (a cubed-sphere hex mesher, or tet refinement towards a point); until then the explicit crate's tests `spheres_collide_as_hertz_says` (a graded cubed-sphere quarter of each sphere, 27 648 hex8: peak force +2.3%, duration −0.4%) and its coarse twin in the main gate check this case on a mesh generated in code | the largest contact force, two steel spheres R = 10 mm (E = 210 GPa, ν = 0.3, ρ = 7.85 t/m³) meeting at 1 m/s (N) = 1005.4; the contact duration (s) = 6.0163e-5 | Hertz's quasi-static impact: with R* = R/2, m* = m/2, E* = E/(2(1 − ν²)), the approach reaches δ = (15 m* v²/(16 E* √R*))^(2/5), the force (4/3) E* √R* δ^(3/2), and the contact lasts 2.9432 δ/v; Hertz, J. reine angew. Math. 92:156–171, 1882; K. L. Johnson, Contact Mechanics, Cambridge 1985, §11.4 |
 | [lid-driven-cavity-re100](../tests/oracle/lid-driven-cavity-re100/) | benchmark | Lid-driven cavity, Re = 100 | lattice Boltzmann CFD (M12) | u/U at y = 0.4531 on the vertical centreline = -0.2109 | Ghia, Ghia and Shin, Journal of Computational Physics 48 (1982) 387–411, Table I (u along the vertical centreline) |
-| [mh-twisted-beam](../tests/oracle/mh-twisted-beam/) | benchmark | MacNeal–Harder twisted beam | shell elements (M8) or mapped blocks with helical edges | tip displacement along the in-plane load = 0.005424; tip displacement along the out-of-plane load = 0.001754 | 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. 6 (p. 8), Table 3 (p. 10) |
+| [mh-twisted-beam](../tests/oracle/mh-twisted-beam/) | benchmark | MacNeal–Harder twisted beam | a helical shell mesh: mesh.block's 2D form is planar and takes z = 0, so the twisted strip must be written node by node (as scordelis-lo-roof-shell and pinched-cylinder are), or mapped blocks must gain helical edges | tip displacement along the in-plane load = 0.005424; tip displacement along the out-of-plane load = 0.001754 | 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. 6 (p. 8), Table 3 (p. 10) |
 | [nafems-le11](../tests/oracle/nafems-le11/) | benchmark | NAFEMS LE11 solid cylinder/taper/sphere under a temperature field | thermal loads (M8 heat transfer) | σ_zz at A = -105 | NAFEMS, The Standard NAFEMS Benchmarks, TNSB Rev. 3, October 1990, test LE11 (target σ_zz = −105 MPa at A) |
 | [nl-cook-membrane](../tests/oracle/nl-cook-membrane/) | benchmark | Cook's membrane, nearly incompressible neo-Hookean, large load (plane strain) | the published finite-strain reference value, transcribed from the paper with its load and material constants | vertical displacement of the top corner C (48, 60) = to be transcribed | R. D. Cook, Improved two-dimensional finite element, J. Struct. Div. ASCE 100(ST9):1851–1863, 1974 (the tapered panel (0, 0), (48, 44), (48, 60), (0, 44), clamped on x = 0, shear on x = 48); finite-strain versions with a neo-Hookean material are published by J. C. Simo, F. Armero, IJNME 33:1413–1449, 1992; the values to compare with are to be transcribed from the paper |
-| [pinched-cylinder](../tests/oracle/pinched-cylinder/) | benchmark | Pinched cylinder with rigid diaphragms | shell elements (M8) | radial displacement under the load = -1.8248e-5 | Belytschko, Stolarski, Liu, Carpenter and Ong, 'Stress projection for membrane and shear locking in shell finite elements', Computer Methods in Applied Mechanics and Engineering 51 (1985) 221–258 (the shell obstacle course); reference 1.8248 × 10⁻⁵ under the load |
-| [pinched-hemisphere](../tests/oracle/pinched-hemisphere/) | benchmark | Hemispherical shell with an 18° hole under alternating point loads | shell elements (M8), or mapped blocks that follow doubly curved faces | displacement under the load along the load = 0.094 | 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. 9 (p. 9), Table 5(b) (p. 11): 0.0940 (lower bound 0.0924 from their [7]) |
-| [scordelis-lo-roof-shell](../tests/oracle/scordelis-lo-roof-shell/) | benchmark | Scordelis–Lo roof with shell elements | shell elements (MITC4, M8) | vertical displacement at the midpoint of the free edge = -0.3024 | 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), Table 5(a) (p. 11); Belytschko, Stolarski, Liu, Carpenter and Ong, 'Stress projection for membrane and shear locking in shell finite elements', Computer Methods in Applied Mechanics and Engineering 51 (1985) 221–258 (the shell obstacle course) |
+| [pinched-hemisphere](../tests/oracle/pinched-hemisphere/) | benchmark | Hemispherical shell with an 18° hole under alternating point loads | a doubly curved shell mesh: mesh.block's 2D form is planar and takes z = 0, so the quarter hemisphere with its 18° polar hole must be written node by node (as scordelis-lo-roof-shell and pinched-cylinder are), or a new patch command must mesh a doubly curved face | displacement under the load along the load = 0.094 | 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. 9 (p. 9), Table 5(b) (p. 11): 0.0940 (lower bound 0.0924 from their [7]) |
 | [taylor-bar](../tests/oracle/taylor-bar/) | experiment | Taylor bar impact (copper) | the measured final shapes, to be transcribed from the paper (explicit Johnson–Cook plasticity is in) | final over initial length = to be transcribed | Wilkins and Guinan, 'Impact of cylinders on a rigid boundary', Journal of Applied Physics 44 (1973) 1200–1206 (final length and mushroom diameter vs impact speed) |