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docs: simplify MITC4 verification and drilling scope

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@@ -8,9 +8,9 @@
- source_numerical_review: `docs/numerical-reviews/linear-static-mitc4-shell-review.md`
- status: `ready-for-numerical-review`
- owner_agent: `formulation-agent`
- date: `2026-08-11`
- revision_basis: numerical review commit `0a5aad4`; findings `NR-C01` through
`NR-C05` and decisions `NR-D01` through `NR-D02`
- date: `2026-08-12`
- revision_basis: approved independent-reference policy, fixed drilling rule, and
removal of calibration gates `NR-O01` through `NR-O04`
- revision_state: `ready-for-numerical-rereview-not-implementation-planning`
- product_execution_scope: `small-strain, small-rotation linear static only`
- future_formulation_scope: `geometrically nonlinear Total Lagrangian residual/tangent; not executable`
@@ -41,11 +41,10 @@ Source labels `S4` and `S4R` both select this one FESA formulation by an approve
semantic mapping. They do not select Abaqus integration or stabilization behavior,
and this document makes no Abaqus formulation-equivalence claim.
Exact drilling reference family/coefficient, drilling-energy warning ratio,
smooth-director angle, and geometry thresholds remain Numerical Review decisions.
The common dimensionless drilling coordinate, geometry-measure inventory,
drilling-load projection tolerance, and normalized algebraic checks are fixed below
by the first Numerical Review. No remaining open symbol is an implementation default.
The drilling rule is fixed below by the approved requirements. Coefficient sweeps,
drilling-energy warnings and datasets, smooth-director calibration (`NR-O03`), and
distortion/warp threshold calibration (`NR-O04`) are outside the implementation gate.
The drilling-load projection and normalized algebraic checks remain fixed below.
## 2. Scope and assumptions
@@ -218,18 +217,10 @@ $$
\mathbf d_I=\frac{\mathbf s_I}{\|\mathbf s_I\|}.
$$
Incident elements are accumulated in the same stable order. After averaging, every
incident deviation
$$
\theta_{eI}=\cos^{-1}\!\left(
\operatorname{clamp}(\mathbf n_e\cdot\mathbf d_I,-1,1)\right)
$$
must satisfy an approved smooth-patch bound `theta_smooth`. The research value
`20 degrees` is only the first Numerical Review candidate. It is not fixed here.
Zero or near-zero cross products and averaged vectors fail using approved
scale-aware tolerances. They are never replaced with a global axis.
Incident elements are accumulated in the same stable order. No additional
`theta_smooth` rejection is applied. Nonfinite or zero cross products and averaged
vectors fail; they are never replaced with a global axis. The pairwise orientation
rule above remains the exact supported-patch predicate.
### 4.3 Deterministic nodal tangent frame
@@ -575,7 +566,7 @@ Duplicate nodes, self-intersection, degenerate midsurface area, and reversed
connectivity are separate fail-closed geometry errors. No failed location is
discarded or replaced by a value from another point.
### 9.3 Scale-aware measures
### 9.3 Basic geometry predicates
Let the consecutive midsurface edge inventory be
@@ -585,73 +576,21 @@ $$
\boxed{L_e=\max_{(I,J)\in\mathcal E}\|\mathbf X_J-\mathbf X_I\|}.
$$
`L_e` must be finite and strictly positive. It is the common element length used by
geometry checks and the DOF scaling in Section 12.5. At every distinct in-plane
location in the center, Gauss, tying, and committed recovery inventory, define
$$
a(\xi,\eta)=\|\mathbf A_\xi\times\mathbf A_\eta\|,
\qquad
\boxed{a_g(\xi,\eta)=\frac{a(\xi,\eta)}{L_e^2}},
$$
$$
\mathbf n_s(\xi,\eta)=
\frac{\mathbf A_\xi\times\mathbf A_\eta}{a(\xi,\eta)},
\qquad
c_d(\xi,\eta)=\mathbf n_s\cdot\overline{\mathbf d}.
$$
`a_g` is the normalized surface-collapse/aspect measure. In particular, for
`A_xi=(1,0,0)` and `A_eta=(0,epsilon,0)` with `L_e=O(1)`, `a_g -> 0` as
`epsilon -> 0`; the angular measure below alone cannot detect that collapse.
At every full three-dimensional validation point, define the dimensionless
angular/director determinant measure
$$
j_s=\frac{J}
{\|\mathbf G_\xi\|\,\|\mathbf G_\eta\|\,\|\mathbf G_\zeta\|}.
$$
For all positive finite point determinants, define the element-variation measure
$$
\boxed{r_J=\frac{J_{min}}{J_{max}}},
\qquad
J_{min}=\min_{p\in\mathcal P_V}J_p,
\quad
J_{max}=\max_{p\in\mathcal P_V}J_p,
$$
and the surface-normal warpage measure relative to the center normal
$$
\boxed{\theta_w=
\max_{p\in\mathcal P_S}
\cos^{-1}\!\left(\operatorname{clamp}
(\mathbf n_s(0,0)\cdot\mathbf n_s(p),-1,1)\right)}.
$$
Here `P_V` contains every volume Gauss point, tying point at `zeta=0`, center, and
every committed bottom/middle/top recovery point; `P_S` contains their distinct
in-plane projections. A valid element must satisfy, without denominator clamping,
`L_e` must be finite and strictly positive. At every center, Gauss, tying, and
committed recovery location required by Section 9.2, the following quantities must
be finite and satisfy
$$
\boxed{
J_p>0,\quad
j_{s,p}>\tau_{ang},\quad
a_{g,p}>\tau_{area},\quad
c_{d,p}>\tau_{dir},\quad
r_J>\tau_{var},\quad
\theta_w<\theta_{warp}.}
\|\mathbf A_\xi\times\mathbf A_\eta\|>0,
\qquad J>0.}
$$
The measures and their location inventory are fixed by this formulation revision.
The positive dimensionless thresholds remain `needs-numerical-calibration`; they
must separate valid distortion/warp sweeps from collapsed negative sequences before
Numerical Review may approve them. No `max(1, geometry_scale)`, zero denominator,
failed-point omission, or pointwise orientation repair is permitted.
The covariant vectors and reciprocal bases must also be finite. Duplicate nodes,
self-intersection, zero-area mappings, and nonpositive determinants fail before
stiffness or recovery is committed. No failed location is omitted, averaged, clamped,
or repaired. This feature defines no calibrated distortion, aspect, warpage, or
director-angle threshold; `NR-O03` and `NR-O04` are not acceptance tests.
## 10. Linear kinematics and MITC4 shear projection
@@ -846,97 +785,40 @@ $$
\mathbf f_{phys}^{24}=\mathbf K_{phys}^{24}\mathbf q_g.
$$
### 12.2 Drilling candidate contract
### 12.2 Fixed drilling stabilization
Let
Let `R` be the index set of the eight director-tangent rotational coordinates in the
physical local ordering `q_20`. Form the finite strictly positive diagonal inventory
$$
\mathbf K_d^l=\operatorname{diag}(k_{d,1},k_{d,2},k_{d,3},k_{d,4}),
\qquad k_{d,I}>0,
\mathcal R_+=\{(K_{20})_{ii}\mid i\in\mathcal R,
(K_{20})_{ii}>0,\ (K_{20})_{ii}\text{ finite}\}.
$$
with rotational-stiffness units `force*length`. The common physical normalization is
Every member has rotational-stiffness units `force*length`. For an otherwise valid
element, an empty `R+` is a deterministic numerical-validation failure. Define
$$
D_{iso}=\frac{Et^3}{12(1-\nu^2)},
\qquad
\boxed{\rho_{d,I}=\frac{k_{d,I}}{D_{iso}}}.
\boxed{k_{ref}=\min\mathcal R_+,\qquad k_d=10^{-3}k_{ref}},
$$
`rho_d,I` is dimensionless and is the only common coordinate for comparing drilling
families. For any candidate `c` written as
and use the same positive scalar at all four local drilling coordinates:
$$
k_{d,I}^{(c)}=\alpha_d^{(c)}k_{ref,I}^{(c)},
\boxed{\mathbf K_d^l=k_d\mathbf I_4}.
$$
the candidate-specific conversion is
Translational diagonals have units `force/length` and shall never enter `R+`.
Off-diagonal entries, nonpositive entries, and nonfinite entries also do not enter
the minimum. The fixed coefficient is a project numerical-stability choice informed
by the thesis rule; it is not a physical constitutive parameter, an Abaqus algorithm,
or a claim of coefficient optimality.
$$
\boxed{
\rho_{d,I}^{(c)}=\alpha_d^{(c)}
\frac{k_{ref,I}^{(c)}}{D_{iso}},
\qquad
\alpha_{d,I}^{eq,(c)}=\rho_{d,I}^{(c)}
\frac{D_{iso}}{k_{ref,I}^{(c)}}.}
$$
The second expression is the nodewise equivalent coefficient for a target `rho_d,I`.
A single actual candidate coefficient may therefore generate a range of `rho_d,I`; that
entire range is part of the calibration evidence. The dimensionally compatible
candidate distributions carried from research are:
1. transverse-shear/area transition family
$$
k_{ref,I}^{(A)}=
\frac{GtA_{eI}}{1+qA_{eI}/t^2},
\qquad q=2.5\times10^{-5},
$$
where
$$
A_{eI}=\int_{A_e}N_I\,dA
\approx\sum_{g=1}^{4}N_I(\xi_g,\eta_g)
\|\mathbf A_\xi\times\mathbf A_\eta\|_g w_g;
$$
2. isotropic bending rigidity
$$
k_{ref}^{(B)}=D_{iso},
\qquad
\rho_{d,I}^{(B)}=\alpha_d^{(B)};
$$
3. a documented positive statistic formed only from the physical rotational block
of `K_20`, whose entries all have `force*length` units, converted by the same
`k_ref/D_iso` ratio. A raw statistic is not comparable until this conversion is
reported.
The first two candidate scales differ sharply in the thin-shell limit:
$$
\boxed{\displaystyle \lim_{A_{eI}/t^2\to\infty}
k_{ref,I}^{(A)}/D_{iso}=6(1-\nu)/q}.
$$
For `nu=0.3` and `q=2.5e-5`, this ratio is `168000`. Consequently the same raw
coefficient, including `10^-3`, cannot represent the same small drilling stiffness
for candidates A and B.
The thesis rule `10^-3 min(all K_ii)` is not admissible because it can mix
translational `force/length` and rotational `force*length` diagonals. A sweep must
instead expand logarithmically in actual `rho_d,I` until it brackets both:
1. a low-side scaled-rank/conditioning or factorization failure; and
2. a high-side physical `U/N/M/Q` contamination boundary.
A nominal value may be proposed only as the smallest point in a stable plateau, with
the adjacent lower and higher decades and separate physical/drilling energies
reported. The reference family, plateau, nominal value, and response/energy bounds
remain `needs-numerical-calibration`; no common `10^-3` center is retained.
There is no `rho_d`, coefficient sweep, stable-plateau selection, conditioning
calibration, artificial-energy ratio, or drilling-specific output contract in this
feature. Verification checks only the exact selection rule, dimensions, symmetry,
positivity, four-mode regularization, deterministic repeatability, and separation
from physical recovery.
### 12.3 Stabilized 24-DOF matrix
@@ -963,13 +845,11 @@ Mass and damping matrices are `N/A` for this linear-static feature.
For a valid free isolated element, the expected physical rank is 14. Embedding it in
24 coordinates creates the six physical rigid modes plus four drilling null modes.
Four positive independent `k_d,I` values should remove only those drilling modes,
The positive uniform `k_d` block should remove only those drilling modes,
giving expected stabilized rank 18 and nullity 6. These are verification targets,
not substitutes for the scaled singular-value/rank study defined in Section 12.5.
The exact-arithmetic rank statement is independent of the calibrated numerical-rank
threshold.
not substitutes for the normalized rigid-action checks defined in Section 17.1.
### 12.4 Energy split
### 12.4 Energy identity
The element energies are
@@ -987,10 +867,9 @@ E_{drill}^e=\frac12\mathbf q_g^T
=\frac12\boldsymbol\gamma^T\mathbf K_d^l\boldsymbol\gamma}.
$$
Both have units `force*length` and are aggregated separately in stable source order.
The ratio `E_drill/E_phys` is reported only when mathematically classifiable. If
`E_phys` is zero or near zero, the two energies are reported explicitly; no arbitrary
denominator clamp is used. The warning ratio remains open.
Both have units `force*length`. `E_drill` is the internal quadratic identity associated
with `K_drill`; it is not a physical shell energy and is not emitted as a required
result. No drilling-energy ratio or warning threshold is defined.
### 12.5 DOF scaling for rank and conditioning evidence
@@ -1032,10 +911,10 @@ $$
\widehat{\mathbf K}_{ff}=\mathbf S_f^T\mathbf K_{ff}\mathbf S_f.
$$
Global condition and numerical-rank evidence uses `K_hat_ff`; a valid `0 x 0 Kff`
Optional global condition and numerical-rank diagnostics use `K_hat_ff`; a valid `0 x 0 Kff`
case is classified separately and is not reported as singular. Numerical
rank/condition thresholds remain calibration decisions, but no raw mixed-unit
matrix may be used to choose them.
condition calibration is not an implementation gate, and no raw mixed-unit matrix
may be used for any reported spectrum or condition estimate.
## 13. Numerical integration
@@ -1501,7 +1380,7 @@ for each shell element in stable source order:
for each shell source node in stable source order:
gather incident candidates in stable element order
reject any nonpositive pairwise incident-normal dot product before averaging
reject degenerate or too-sharp incident normals
reject nonfinite or zero incident normals and averaged vectors
d_I = normalize(sum(A_e * n_e))
select least-aligned global axis with deterministic tie break
construct right-handed (a_I, b_I, d_I)
@@ -1515,7 +1394,7 @@ build T, T_p, T_d
initialize K20[20,20] = 0
evaluate the complete center/Gauss/tying/recovery geometry inventory
validate pointwise J, j_s, a_g, c_d and aggregate r_J, theta_w
validate finite nonzero surface area and finite positive J at every required location
evaluate and validate four midsurface tying locations
for each 2x2 midsurface Gauss location in fixed order:
construct and validate local frame (e1,e2,e3)
@@ -1530,20 +1409,21 @@ for each 2x2 midsurface Gauss location in fixed order:
check K20 finite and symmetric within approved normalized tolerance
Kphys24 = T_p^T * K20 * T_p
construct positive Kd_local and report every k_d,I through rho_d,I = k_d,I/D_iso
collect positive finite tangent-rotation diagonals R+ from K20
require R+ nonempty; k_d = 1e-3 * min(R+); Kd_local = k_d * I4
Kdrill24 = T_d^T * Kd_local * T_d
Ke24 = Kphys24 + Kdrill24
form S20, S24, Khat20, and Khat_e for rank/conditioning evidence only
form S20, S24, Khat20, and Khat_e for normalized algebraic evidence only
fint24 = Ke24 * q_g
residual24 = fint24 - f_CLOAD
return matrices, residual, transforms, frames, and separate energy operators
return matrices, residual, transforms, and frames
```
### 16.3 Global linear-static lifecycle
```text
assemble all Ke24 contributions with stable element-local COO ordering
form model-length DOF scaling and Khat_ff for global rank evidence only
form model-length DOF scaling and Khat_ff for optional normalized diagnostics only
partition full K into Kff, Kfc, Kcf, Kcc in stable free/constrained order
factorize Kff before load assembly
assemble and deterministically aggregate nodal CLOAD
@@ -1551,7 +1431,7 @@ accept an exact-zero nodal moment separately; otherwise require rho_M <= 1e-12
solve Kff * df = Ff - Kfc * dc
reconstruct full displacement d
compute full residual r = K*d - F
recover shell rows and physical/drilling energies in stable source order
recover shell rows and physical shell energy in stable source order
validate complete finite candidate state/output, then commit
```
@@ -1565,7 +1445,7 @@ for each element and each 2x2 midsurface location in fixed order:
attach exact natural coordinates, section position, frame, and source identity
recover nodal global U/UR and full-residual RF/RM
compute E_physical and E_drill separately; never clamp a near-zero denominator
compute required physical shell energy; emit no drilling-specific result
```
### 16.5 Future nonlinear tangent check
@@ -1587,14 +1467,15 @@ given an approved global Phi map, objective drill potential, and load work:
- Shape-function partition of unity, Kronecker delta, and derivative sums.
- Nodal and integration frames orthonormal and right-handed.
- The complete `J/j_s/a_g/c_d/r_J/theta_w` inventory at center, Gauss, tying,
and committed recovery points.
- Finite nonzero surface area and finite positive `J` at every center, Gauss, tying,
and committed recovery point.
- Scaled `K20`, `Kphys24`, `Kdrill24`, and `Ke24` symmetry and spectrum.
- Transformation work/energy invariance.
- Physical rigid modes satisfy normalized scaled stiffness action.
- Stabilized free-element nullity is exactly six; accepted non-rigid physical modes
have positive physical energy.
- Pure drill vectors have zero physical energy and positive drilling energy.
- Pure drill vectors have zero physical-shell energy and positive action under the
fixed numerical drilling block.
- Consistent force/length unit rescaling leaves dimensionless decisions unchanged.
For any nonzero scaled stiffness under test, the approved normalized checks are
@@ -1634,41 +1515,35 @@ Independently verify:
- pure twist and `K12/M12` convention;
- zero strain/resultant/stress contribution from a pure drilling vector.
### 17.3 Locking, distortion, and curved shells
### 17.3 Nonblocking accuracy studies
- Thin and thick plate/shell mesh and thickness sequences are required; one
displacement on one mesh is insufficient.
- Distorted and warped valid quadrilaterals must be swept through approved geometry
measures.
- Original MITC4 controls transverse-shear locking but can retain membrane locking
in distorted curved meshes. This is a known limitation, not permission to add
MITC4+.
- Preferred nodal-load-compatible curved benchmarks are the pinched cylinder and
NAFEMS LE3 hemispherical shell. Scordelis-Lo is admissible only after an equivalent
nodal-load adaptation is documented.
Thin/thick, distorted, warped, pinched-cylinder, NAFEMS LE3 and Scordelis-Lo studies
remain useful for documenting the original MITC4 element's known shear- and
membrane-locking limits. They are not required implementation-completion tests and
do not authorize MITC4+ or an expanded input subset. `NR-O03` and `NR-O04` are
explicitly removed from the acceptance scope.
### 17.4 Drilling sensitivity
### 17.4 Fixed drilling checks
For every candidate reference scale, convert candidate coefficients to the actual
nodewise `rho_d,I` inventory. Expand a logarithmic sweep until both the low-side
rank/conditioning failure and high-side physical-response contamination boundary
are observed, and record:
For representative valid element kernels, verify:
- free-element scaled rank and scaled constrained-system conditioning;
- global `U` and physical `N/M/Q` sensitivity;
- `E_phys` and `E_drill` without denominator clamping;
- invariance under consistent unit conversion, thickness ratios, and mesh sizes.
- `R+` contains only finite positive physical tangent-rotation diagonals;
- `k_d=10^-3 min(R+)` and `K_d^l=k_d I4` exactly;
- `K_drill^24` is symmetric and positive on each pure drilling coordinate;
- four nonphysical drilling null modes are removed while the six physical rigid
modes satisfy the normalized action test;
- physical generalized strain, resultant and stress recovery is unchanged by a
pure drilling vector.
Candidate runs are compared by overlapping actual `rho_d,I` ranges, never by equal
raw `alpha_d`. The study must select the reference family, the smallest stable
plateau value, its adjacent-decade sensitivity, and the energy warning criterion
before Implementation Planning.
No coefficient sweep, plateau, condition threshold, response-sensitivity criterion,
or drilling-energy warning is part of this check.
### 17.5 Reference-comparison boundary
Abaqus comparisons block only on matched global `U1/U2/U3` rows under the approved
mixed tolerance decided downstream. `UR1/UR2/UR3` is fully reported and may emit a
deterministic nonblocking large-error warning, but it does not change pass/fail.
Abaqus comparisons block only on matched global `U1/U2/U3` rows under
`tolerance_c=1e-9+1e-6*reference_scale_c`, where `reference_scale_c` is the maximum
absolute finite Abaqus value for the same component. `UR1/UR2/UR3` uses the same
formula but an exceedance emits only a deterministic nonblocking warning.
FESA `S4` and `S4R` inputs must produce the same internal numerical rows for identical
supported models while preserving distinct source metadata. Abaqus S4 and S4R are
not expected to be numerically identical on finite meshes.
@@ -1686,16 +1561,15 @@ procedure.
| Risk | Consequence | Required control |
| --- | --- | --- |
| Transverse-shear locking | overly stiff thin-shell response | exact edge-midpoint MITC projection and thickness/mesh convergence |
| Membrane locking on distorted curved meshes | slow or nonuniform convergence | distortion/curvature sweeps; document original MITC4 limitation |
| Transverse-shear locking | overly stiff thin-shell response | exact edge-midpoint MITC projection and patch/reference evidence; broader convergence is a known limitation study |
| Membrane locking on distorted curved meshes | slow or nonuniform convergence | document original MITC4 limitation; optional later studies do not alter the current gate |
| Volumetric locking | N/A for the approved plane-stress shell contract | do not infer a three-dimensional incompressible formulation |
| Wrong tying pair or engineering-shear factor | swapped/incorrect shear and loss of patch consistency | component-level tying and patch tests |
| Reversed or degenerate Jacobian | invalid basis, sign, or energy | common location inventory with `J/j_s/a_g/c_d/r_J/theta_w` |
| Reversed or degenerate Jacobian | invalid basis, sign, or energy | finite nonzero surface area and finite positive `J` at every required location |
| Discontinuous shared director | artificial coupling or undefined frame | reject; require duplicate nodes at folds |
| Fixed-axis tangent singularity | nondeterministic rotation transform | least-aligned global-axis construction |
| Drilling coefficient too small | rank/conditioning failure | rank and conditioning sensitivity sweep |
| Drilling coefficient too large | contaminated displacement/resultant | physical-output and separate-energy sensitivity sweep |
| Mixed-unit drilling or spectrum scale | unit-dependent stabilization/rank | use `rho_d,I` and `S^T K S`; prohibit raw mixed-unit comparison |
| Invalid drilling reference inventory | absent or nonpositive numerical regularization | require nonempty finite positive physical rotational diagonals and fail deterministically otherwise |
| Mixed-unit drilling scale | unit-dependent stabilization | exclude every translational diagonal; use only the physical tangent-rotation block |
| Misconstructed rigid test | false drill energy in a physical mode | use rigid translation plus tangent director change with `gamma=0` |
| Recovery/stiffness mismatch | inconsistent energy and section output | same frames, tying, material, and thickness rule |
| Location averaging | hidden sign/identity error | preserve exact location rows; no nodal extrapolation |
@@ -1748,25 +1622,25 @@ research brief remain the project source of truth.
| Requirement group | Formulation coverage | Remaining owner |
| --- | --- | --- |
| `001-004`, `030`, `037` | linear-static boundary; S4/S4R one FESA path, source identity distinct | I/O, planning |
| `005`, `031-038` | 24 global DOFs; 20 physical plus four drill coordinates; `rho_d,I`, scaled rank, energy | Numerical Review for drill calibration |
| `005`, `031-038` | 24 global DOFs; 20 physical plus four drill coordinates; fixed positive rotational-diagonal stabilization | Numerical Review for formula consistency |
| `006-010` | isotropic plane stress, one centered constant-thickness layer | I/O validation |
| `011-016` | pairwise normals, deterministic averaging/frames, complete geometry measures | Numerical Review for calibrated thresholds |
| `011-016` | pairwise orientation, deterministic averaging/frames, basic finite/positive geometry predicates | I/O validation |
| `017-020` | global 24-DOF virtual work; `rho_M <= 1e-12`; distributed loads excluded | I/O diagnostic/schema |
| `024-029` | deterministic element buffers, partitioned linear lifecycle, full-residual reaction | planning |
| `039-048` | nodal/global and shell/local recovery inventory, units, identities, energy split | I/O schema |
| `049-057` | scaled normalized invariants, patches, locking, geometry, curved shells, drilling, equilibrium | Numerical Review/reference/physics |
| `058-064` | U blocking, UR warning-only comparison boundary | Numerical Review/reference model |
| `065-072` | reference immutability and displacement-only evidence boundary acknowledged | reference model |
| `039-048` | nodal/global and shell/local recovery inventory, units, identities, physical shell energy | I/O schema |
| `049-057` | normalized invariants, patches, fixed drilling, declared references and equilibrium | Numerical Review/reference/physics |
| `058-064` | exact B33 mixed tolerance; U blocking and UR warning-only | reference verification |
| `065-072` | exact existing S4/S4R paths, immutability and displacement-only boundary | reference model |
### 20.1 Numerical Review revision traceability
The first review findings map to this revision as follows.
`NR-C01` maps to Sections 9.2-9.3, 16.2, and 17.1/17.3. The geometry measures
are fixed while their thresholds still require calibration.
`NR-C01` maps to Sections 9.2-9.3, 16.2, and 17.1/17.3. Basic point inventory and
finite/positive predicates remain; `NR-O03`/`NR-O04` calibration is removed.
`NR-C02` maps to Sections 12.2 and 17.4. The common `rho_d,I` coordinate and
candidate conversions are fixed while the stable plateau remains open.
`NR-C02` maps to Sections 12.2 and 17.4. The project decision replaces candidate
normalization and plateau work with the exact fixed rotational-diagonal rule.
`NR-C03` maps to Sections 12.3/12.5 and 17.1. Element/global DOF scaling is fixed
while the numerical-rank threshold remains open.
@@ -1781,53 +1655,45 @@ normalized algebraic metrics.
## 21. Open issues and downstream handoff
### 21.1 Blocking Numerical Review decisions
### 21.1 Current numerical-review boundary
1. Select the dimensionally compatible drilling reference-scale family.
2. Select the nodewise `rho_d,I` stable plateau, nominal value, scaled
conditioning/rank acceptance, and physical-output contamination bound.
3. Define classification and warning behavior for `E_drill/E_phys`, including the
zero/near-zero physical-energy case.
4. Approve `theta_smooth` after curved-mesh resolution sweeps; `20 degrees` is only
the initial candidate.
5. Calibrate thresholds for the fixed `J/j_s/a_g/c_d/r_J/theta_w` geometry
inventory using valid distortion/warp and collapsed negative sequences.
6. Jointly with Reference Model, approve the U mixed tolerance and nonblocking UR
large-error warning threshold.
The first review already approved `rho_M <= 1e-12`, the normalized algebraic checks,
the MITC tying/component signs, constitutive law, quadrature, and recovery signs.
This revision is ready for Numerical Review rerun but not for Implementation
Planning until the six remaining evidence-backed decisions are closed.
No calibration decision remains open for the linear implementation. The first review
approved `rho_M <= 1e-12`, the normalized algebraic checks, MITC tying/component signs,
constitutive law, quadrature, and recovery signs. The approved policy fixes drilling
and U/UR tolerance and removes drilling-energy calibration plus `NR-O03`/`NR-O04`.
Numerical Review shall now check internal consistency and may not treat those removed
items or an expanded reference portfolio as missing evidence.
### 21.2 I/O Definition handoff
- Preserve source `S4`/`S4R` separately from internal `FESA-MITC4`.
- Define exact keyword subset, section/material resolution, and fail-closed
diagnostics for director, folds, Jacobians, unsupported loads, and recovery;
diagnostics for director orientation, basic topology/Jacobians, unsupported loads, and recovery;
encode exact-zero nodal moment separately and enforce `rho_M <= 1e-12` without
a denominator clamp.
- Define exact HDF5 row schemas for global `U/UR`, `RF/RM`; four midsurface
generalized-strain/resultant locations; bottom/middle/top stress positions; full
residual/equilibrium; and separate energies.
residual/equilibrium; and physical shell energy. Do not add drilling-specific datasets.
- Preserve local frame and natural-coordinate identity without location averaging.
### 21.3 Reference Model handoff
- Use at least one S4 and one S4R source artifact, but compare formulation-independent
global displacement evidence rather than claiming element equivalence.
- Prioritize pinched cylinder and NAFEMS LE3 models compatible with nodal loads and
approved BC semantics.
- Propose the mixed U tolerance and nonblocking UR warning threshold.
- Record the existing `reference/shell/` S4 and `reference/shellR/` S4R input and
displacement CSV paths, but compare only formulation-independent global displacement
evidence rather than claiming element equivalence.
- Use the exact B33 mixed tolerance; do not add administrative metadata or portfolio gates.
- Do not create, repair, rename, or run reference artifacts during this formulation
gate.
### 21.4 Implementation Planning handoff
- Do not begin until Numerical Review closes Section 21.1.
- Begin after the Numerical Review, I/O contract, and lightweight Reference Model
inventory agree with this formulation.
- Translate the deterministic preprocessing, 24-to-20 transform, tying projection,
physical/drill split, quadrature, recovery, and invariant portfolio into
`RED -> GREEN -> VERIFY` tests before production changes.
fixed physical/drill split, quadrature, recovery, and required invariants into
Harness Step drafts with `RED -> GREEN -> VERIFY` tests before production changes.
- Obtain user approval of the multi-Step draft before creating phase-planning files;
Harness execution requires a separate explicit user request.
- Keep future nonlinear state and tangent out of the current linear-static plan.
### 21.5 Future nonlinear formulation handoff