diff --git a/docs/formulations/mitc4-shell-formulation.md b/docs/formulations/mitc4-shell-formulation.md index 19a1166..5f736ad 100644 --- a/docs/formulations/mitc4-shell-formulation.md +++ b/docs/formulations/mitc4-shell-formulation.md @@ -6,12 +6,12 @@ - source_requirement: `docs/requirements/linear-static-mitc4-shell.md` - source_research: `docs/research/linear-static-mitc4-shell-research.md` - source_numerical_review: `docs/numerical-reviews/linear-static-mitc4-shell-review.md` -- status: `ready-for-numerical-review` +- status: `approved-for-implementation-planning` - owner_agent: `formulation-agent` - 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` +- revision_state: `numerical-review-passed` - product_execution_scope: `small-strain, small-rotation linear static only` - future_formulation_scope: `geometrically nonlinear Total Lagrangian residual/tangent; not executable` diff --git a/docs/io-definitions/linear-static-mitc4-shell-io.md b/docs/io-definitions/linear-static-mitc4-shell-io.md index 47fc717..e7f2d93 100644 --- a/docs/io-definitions/linear-static-mitc4-shell-io.md +++ b/docs/io-definitions/linear-static-mitc4-shell-io.md @@ -8,13 +8,13 @@ - source_formulation: `docs/formulations/mitc4-shell-formulation.md` - source_numerical_review: `docs/numerical-reviews/linear-static-mitc4-shell-review.md` - source_commits: requirements/research/formulation policy revision `73df844` -- status: `approved-ready-for-numerical-review` +- status: `approved-for-implementation-planning` - owner_agent: `io-definition-agent` - date: `2026-08-12` - authoritative_output: `results.h5` - hdf5_schema_version: `0` - reference_cases: read-only S4 at `reference/shell/`; read-only S4R at `reference/shellR/` -- implementation_planning_authorized: `false` +- implementation_planning_authorized: `true` This document defines the approved semantic input and output contract for the linear-static MITC4 shell feature. It does not define parser, model, HDF5-writer, or @@ -650,7 +650,8 @@ administration and reference-portfolio expansion are removed scope. ### 11.4 Implementation Planning Agent -- Do not start while `implementation_planning_authorized=false`. +- Planning is authorized by the numerical review; implementation and Harness execution + remain separately unauthorized until explicitly requested. - After approval, convert every supported/unsupported keyword row, source identity, geometry/director error, drilling-load projection, exact HDF5 path/shape/order, atomic failure, source-row normalization, and U-versus-UR decision into diff --git a/docs/numerical-reviews/linear-static-mitc4-shell-review.md b/docs/numerical-reviews/linear-static-mitc4-shell-review.md index 3c632fd..0c40068 100644 --- a/docs/numerical-reviews/linear-static-mitc4-shell-review.md +++ b/docs/numerical-reviews/linear-static-mitc4-shell-review.md @@ -3,818 +3,344 @@ ## Metadata - feature_id: `linear-static-mitc4-shell` -- source_requirement: `docs/requirements/linear-static-mitc4-shell.md` -- source_research: `docs/research/linear-static-mitc4-shell-research.md` - source_formulation: `docs/formulations/mitc4-shell-formulation.md` -- source_commits: requirements `5c3025a`, research `02680dc`, formulation revision - `6cb0302`, prior numerical review `ebb2657`, I/O definition `73dc761`, reference - metadata policy `2bd297d`, S4 legacy artifacts `57122b0`, observed S4R artifacts - `a28dba4` -- source_formulation_sha256: `6DD807E7D9D02C2454CAAF0289E391F5812CC309CDF1C00E92ACEAA97841957D` +- source_requirements: `docs/requirements/linear-static-mitc4-shell.md` +- source_research: `docs/research/linear-static-mitc4-shell-research.md` - source_io_definition: `docs/io-definitions/linear-static-mitc4-shell-io.md` -- source_io_definition_sha256: `081AB60E504382F2A52C3170FF1F599A1B3E312143065E80F7AD467558958BA3` -- status: `needs-reference-model` -- review_iteration: `3` +- source_reference_inventory: `docs/reference-models/linear-static-mitc4-shell-reference-models.md` +- repository_policy: `AGENTS.md`, `docs/ADR.md`, `docs/ARCHITECTURE.md`, + `docs/SOLVER_AGENT_DESIGN.md` +- reviewed_revisions: `73df844`, `22a3238` +- status: `pass-for-implementation-planning` - owner_agent: `numerical-review-agent` - date: `2026-08-12` -- implementation_planning_authorized: `false` -- review_scope: `현재 선형 정적 formulation 전체 및 미래 기하비선형 tangent 절의 수학 구조` -- reference_artifact_state: `reference/shell/` S4 4 files and `reference/shellR/` - S4R 4 files observed read-only; both lack `metadata.json`, which is - `absent-allowed`; both also lack the generally required bundle `README.md`, and - the feature-specific Reference Model Contract is absent +- implementation_planning_authorized: `true` +- implementation_complete: `false` +- reference_comparison_complete: `false` ## Review Verdict -- verdict: `needs-reference-model` -- primary_reason: 1차 리뷰의 confirmed formulation defect `NR-C01`-`NR-C05`와 - 결정 `NR-D01`-`NR-D02`는 revision `6cb0302`에 수학적으로 일관되게 반영되었다. - S4/S4R artifact 존재성도 현재 확인되었다. 그러나 두 bundle은 동일한 - 평면 정규 `6 x 6` mesh의 단일 두께 사례이며, 승인된 MITC4 Reference - Model Contract, provenance/unit/step-frame 계약, U/UR tolerance 제안, - drilling sweep, geometry/director separation sweep이 없다. 따라서 존재하는 - artifact는 source-type presence만 닫고 Implementation Planning 수치 gate를 - 닫지 못한다. -- secondary_dependencies: `needs-numerical-calibration` -- current_linear_kernel_assessment: MITC4의 20-DOF 물리 kinematics, covariant shear - tying, plane-stress constitutive law, `2 x 2 x 2` integration, 24-DOF 변환 및 recovery의 - 중심 수학 구조와 수정된 weak form, geometry measure, DOF scaling 계약은 타당하다. -- future_nonlinear_assessment: Total Lagrangian residual과 material/geometric tangent의 - 변분 구조와 일반 좌표 사상 `q20=Phi(qg)`의 Hessian 항은 타당하다. 다만 실제 - finite-director chart/update 및 objective drilling potential은 의도적으로 미확정이며 - 미래 기하비선형 구현은 계속 금지한다. +- verdict: `pass-for-implementation-planning` +- reason: The current linear-static formulation closes the physical 20-DOF MITC4 + kernel, its global 24-DOF embedding, fixed drilling regularization, Jacobian and + quadrature rules, residual/stiffness equations, recovery signs, and verification + invariants without a mathematical inconsistency in the approved feature scope. +- critical_blockers: `none` +- remaining_formulation_revisions: `none for the current linear-static scope` +- downstream_boundary: Implementation Planning may begin. This verdict does not + claim implementation, build/test, reference-comparison, physics-sanity, or release + completion. -현재 선형 정적 정식화에서 새 confirmed mathematical defect는 발견되지 않았다. -다만 `pass-for-implementation-planning`은 미정 상수를 임의 default로 넘겨도 -된다는 뜻이 아니다. 요구조건 `036`, `056`, `058`-`062`와 formulation -Section 21.1이 명시적으로 요구하는 evidence가 없으므로 -`implementation_planning_authorized=false`를 유지한다. 다음 rerun은 승인된 -Reference Model Contract와 수치 calibration evidence가 준비된 뒤 수행해야 한다. +The future geometrically nonlinear material in Formulation Section 15 remains +explicitly non-executable. Its unresolved global finite-rotation map and objective +drilling potential do not block the current linear-static implementation plan. -## 1. Review Method and Evidence Boundary +## Critical Findings -검토는 다음 순서로 수행했다. +No confirmed mathematical defect remains in the approved linear-static formulation. +The previous review's `needs-reference-model` verdict is not a valid current +formulation verdict: the current numerical-review gate is based on numerical and +formulation consistency, while downstream artifact administration and comparison +execution are separate gates. -1. 요구조건의 단위, DOF, rigid mode, tolerance 및 output 계약을 formulation과 대조했다. -2. 원 MITC4 문헌의 director interpolation, edge-midpoint shear tying, full integration, - rigid mode 및 nonlinear incremental 식과 대조했다. -3. 각 matrix block의 차원, 변환의 virtual-work 보존, 부호 및 component order를 - 독립적으로 재유도했다. -4. 1차 리뷰의 geometry collapse, drilling 박판 극한, 혼합 DOF scaling 및 nonlinear - coordinate-map 반례를 수정본에 다시 적용했다. -5. I/O 계약과 project-wide optional `metadata.json` policy를 현재 artifact - inventory에 대조했다. -6. 두 input의 키워드, mesh/property/load 동일성, CSV row count, - finite/unique node identity, hash와 displacement component scale을 read-only로 - 확인했다. -7. 확인된 결함의 해소 여부, 알려진 위험, 근거가 부족한 open decision을 분리했다. +### 1. Previous finding disposition -코드, Harness, Abaqus 및 reference solver는 실행하지 않았고 formulation 문서는 -수정하지 않았다. 이 리포트는 reference comparison이나 release 승인이 아니다. +| previous item | current disposition | evidence and strict consequence | +| --- | --- | --- | +| `NR-C01` Jacobian/geometry inventory | resolved | Formulation Sections 9.2-9.3 enumerate center, stiffness, tying, and recovery locations and require finite bases, nonzero area, and `J>0`; Requirements 014/016 intentionally define no calibrated smooth-angle, distortion, or warp threshold. | +| `NR-C02` drilling normalization | resolved | Formulation Section 12.2 and Requirements 033-036 now define one exact dimensional rule using only positive physical tangent-rotation diagonals. No calibration decision remains. | +| `NR-C03` mixed-DOF algebraic scaling | resolved | Formulation Sections 12.3 and 12.5 define physical length scaling separately from the physical/drilling stiffness split and provide normalized rank, symmetry, and rigid-action evidence. | +| `NR-C04` 20/24-DOF weak-form mismatch | resolved | Formulation Sections 5.2-5.3 and 7.1-7.2 place physical, drilling, and external work in the common global 24-DOF test space using the required transpose maps. | +| `NR-C05` nonlinear global tangent closure | resolved for current scope | Formulation Section 15 now labels the nonlinear equations non-executable and identifies the missing nonlinear `Phi` map, map Hessian, and objective drilling potential. Those items block only a future nonlinear feature. | +| `NR-D01` drilling-direction nodal moment | retained/resolved | The exact-zero branch and `rho_M=|d dot M|/||M|| <= 1e-12` rule are consistent in Formulation Section 6.2 and I/O Section 4.3. | +| `NR-D02` normalized algebraic checks | retained/resolved | Formulation Section 17.1 defines scale-aware symmetry, rigid-action, frame, transformation-energy, residual, and equilibrium checks without a denominator clamp. | +| `NR-O01` drilling coefficient/plateau | resolved by approved fixed rule | `k_d=10^-3 min(R+)` replaces the former coefficient-family/sweep question. A sweep, plateau, response sensitivity, or condition-number calibration is not an acceptance gate. | +| `NR-O02` drilling-energy warning | removed from approved scope | Drilling is an internal numerical potential only. No drilling-energy ratio, warning threshold, or drilling-specific output is required. | +| `NR-O03` smooth-director angle | removed from approved scope | Requirements 014/054 and Formulation Sections 4.2 and 9.3 use exact orientation/finite/nonzero predicates and explicitly remove `NR-O03`. It is not an open numerical decision. | +| `NR-O04` distortion/warp calibration | removed from approved scope | Requirements 016/054 and Formulation Sections 9.2-9.3 require exact finite/positive validity checks and explicitly remove `NR-O04`. It is not an open numerical decision. | +| `NR-O05` U/UR tolerance | resolved | Requirements 058-062, Formulation Section 17.5, I/O Section 7.6, and Reference Case Section 5 all use the exact approved B33 component-scale formula. | -## 2. First-review Findings and Rerun Disposition +### 2. Required policy classifications -이 절은 1차 리뷰의 발견 근거를 보존한다. 각 finding 본문의 현재형 서술과 -`Required revision`은 formulation commit `67251e0`에 대한 역사적 기록이며, 현재 -판정은 각 항목 끝의 `Rerun disposition`이 지배한다. +#### 2.1 Fixed drilling rule — resolved and implementation-ready -| finding/blocker | rerun status | current evidence | remaining boundary | -| --- | --- | --- | --- | -| `NR-C01` | resolved | Sections 9.2-9.3, 16.2, 17.1/17.3 | fixed measure threshold calibration | -| `NR-C02` | resolved | Sections 12.2, 17.4 | drilling family/plateau calibration | -| `NR-C03` | resolved | Sections 12.3/12.5, 17.1 | numerical rank/conditioning evidence | -| `NR-C04` | resolved | Sections 7.1-7.2 | none for current linear formulation | -| `NR-C05` | resolved | Sections 15.1-15.5, 17.6 | current linear scope only; actual nonlinear chart/update remains future-only | -| `NR-O01` | open | dimensionless `rho_d` contract only | family, sweep, stable plateau, nominal coefficient, scaled rank/conditioning bound | -| `NR-O02` | open | separate energy and zero-denominator classification only | warning threshold and physical-response contamination bound | -| `NR-O03` | open | current artifacts have a flat common normal field | curved-mesh incident-normal distribution and hard `theta_smooth` acceptance | -| `NR-O04` | open | fixed geometry-measure inventory and one regular planar mesh | valid distortion/warp versus collapsed/inverted separation sweep and thresholds | -| `NR-O05` | partially resolved | S4/S4R U/UR rows and component scales are observable | approved unit/provenance contract, mesh/convergence evidence, U mixed tolerance, UR warning threshold | -| reference source-type presence | resolved | S4 and S4R inputs plus displacement CSVs are both present | presence is not usability or numerical calibration | -| Reference Model Contract/artifact usability | open | no feature-specific contract; both bundle READMEs are absent; S4R path is noncanonical under current I/O contract | approved alias/canonical disposition, required README handling, provenance, units, step/frame, schema, tolerance | -| `metadata.json` policy | resolved | absent in both bundles and optional by project policy | absence is `absent-allowed`; only a present/conflicting file would require action | - -### NR-C01 — Resolved — Jacobian geometry measure completeness - -Formulation은 - -$$ -j_s=\frac{J} -{\|\mathbf G_\xi\|\,\|\mathbf G_\eta\|\,\|\mathbf G_\zeta\|} -$$ - -와 `J_min/J_max`를 제안한다. 다음 직교 mapping을 고려한다. - -$$ -\mathbf G_\xi=(1,0,0),\qquad -\mathbf G_\eta=(0,\varepsilon,0),\qquad -\mathbf G_\zeta=(0,0,t/2),\qquad \varepsilon>0. -$$ - -그러면 - -$$ -J=\varepsilon t/2, -\qquad j_s=1, -\qquad J_{min}/J_{max}=1 -$$ - -이므로 `epsilon -> 0`인 near-collapsed element도 두 무차원 지표를 모두 완전히 -통과한다. `J>0`은 exact zero만 배제하고 user-consistent unit에서 near-zero를 판정할 -기준이 되지 않는다. Formulation에 “degenerate area를 별도 거부”한다고 적혀 있지만 -그 scale-aware measure와 threshold가 수식 또는 알고리즘으로 정의되지 않았다. - -이는 `FESA-REQ-LSMITC4-016`의 near-singular Jacobian 거부를 구현할 수 없게 하는 -confirmed defect다. [[MITC Shell Kinematics]]의 degenerated mapping은 valid reciprocal -basis를 전제로 하고, [[Shell Locking Phenomenon]]이 지적하는 distortion 위험도 -geometry acceptance가 실제 collapse를 식별할 것을 요구한다. - -Required revision: - -- 다음 세 종류를 분리해 모두 정의해야 한다. - - angular/director measure: 현재 `j_s` 계열; - - surface-collapse/aspect measure: - -$$ -a_g=\frac{\|\mathbf A_\xi\times\mathbf A_\eta\|}{L_e^2}, -\qquad -L_e=\max_{edge\ (I,J)}\|\mathbf X_J-\mathbf X_I\|; -$$ - - - variation/warp measure: `J_min/J_max`와 Gauss/center normal deviation. -- exact threshold는 distortion sweep에서 정하되, measure 자체는 formulation에 먼저 - 고정해야 한다. -- center, Gauss, tying 및 committed recovery point가 동일한 orientation/validity - inventory를 사용해야 한다. - -Rerun disposition: `L_e`, `a_g`, `j_s`, `c_d`, `r_J`, `theta_w`와 공통 point inventory가 -고정되었다. `epsilon -> 0` 직교 collapse에서 `j_s=1`이어도 `a_g=epsilon/4 -> 0`이므로 -기존 반례를 검출한다. 정확한 threshold는 여전히 calibration 대상이나 measure 누락 -결함은 해소되었다. - -### NR-C02 — Resolved — common drilling normalization - -Formulation의 후보 A와 B는 모두 `force*length` 차원을 가져 dimensional consistency는 -만족한다. 그러나 얇은 쉘 극한에서 두 기준의 크기는 매우 다르다. 후보 A는 - -$$ -k_{ref}^{(A)} -=\frac{GtA}{1+qA/t^2} -\xrightarrow[A/t^2\to\infty]{} -\frac{Gt^3}{q}, -$$ - -후보 B는 - -$$ -D_{iso}=\frac{Et^3}{12(1-\nu^2)}. -$$ - -따라서 - -$$ -\boxed{ -\frac{k_{ref}^{(A)}}{D_{iso}} -\to\frac{6(1-\nu)}{q}} -$$ - -이고 `nu=0.3`, `q=2.5e-5`이면 그 비는 `168000`이다. 동일한 -`alpha_d=1e-3`을 곱하면 후보 A의 drilling stiffness는 약 `168 D_iso`가 되지만 -후보 B는 `0.001 D_iso`가 된다. 동일한 `10^-3` 중심 sweep은 서로 같은 “작은 -drilling” 영역을 비교하지 않는다. - -Formulation 17.4절의 “모든 후보를 research order 주변에서 sweep”은 이 차이를 -제거하지 못한다. `10^-3`은 thesis의 다른 reference scale에 붙은 사례이며 후보 A와 -B의 공통 coefficient가 아니다. - -Required revision: - -- 후보 비교의 독립 변수는 raw `alpha_d`가 아니라 - -$$ -\rho_{d,I}=\frac{k_{d,I}}{D_{iso}} -$$ - - 또는 승인된 physical rotational-block scale에 대한 동등한 무차원 비로 정의한다. -- 각 후보의 `alpha_d <-> rho_d` 변환을 명시한다. -- sweep은 하나의 임의 중심값을 공유하지 말고, 낮은 쪽 rank/conditioning 실패와 - 높은 쪽 physical response contamination을 모두 관찰할 때까지 로그 범위를 - 확장한다. -- nominal value는 stable plateau의 가장 작은 값으로 선택하고, 인접 decade에서 - `U/N/M/Q`와 energy의 민감도를 기록한다. - -Research는 exact Abaqus small factor를 제공하지 못하며 이 gap을 정직하게 기록했다. -따라서 source 인용만으로 coefficient를 고를 수 없고 numerical calibration evidence가 -필요하다. - -Rerun disposition: `rho_d,I=k_d,I/D_iso`, 후보별 변환, logarithmic bracketing 및 -smallest-stable-plateau 규칙이 고정되었다. 문서의 박판 극한 -`6(1-nu)/q=168000`도 독립 재계산과 일치한다. 실제 후보/plateau/nominal 값은 -의도적으로 `needs-numerical-calibration`에 남는다. - -### NR-C03 — Resolved — mixed-DOF scaling contract - -Shell stiffness의 block 단위는 서로 다르다. - -| block | units | -| --- | --- | -| translation-translation | `force/length` | -| translation-rotation | `force` | -| rotation-rotation | `force*length` | - -따라서 raw `K20` 또는 `K24`의 singular value/eigenvalue와 condition number는 길이 -단위 변경에 불변하지 않다. Formulation은 혼합 단위 diagonal minimum을 올바르게 -금지했지만, rank/conditioning study에는 같은 문제를 해결하는 scaling을 정의하지 -않았다. - -Required revision: - -$$ -\mathbf q=\mathbf S_e\widehat{\mathbf q}, -\qquad -\mathbf S_e=\operatorname{blockdiag}_{I=1}^{4} -\left(L_e\mathbf I_3,\mathbf I_3\right), -$$ - -$$ -\boxed{ -\widehat{\mathbf K}_e=\mathbf S_e^T\mathbf K_e\mathbf S_e}. -$$ - -`K_hat`의 모든 성분은 `force*length` 단위를 가지므로 normalized rank와 spectrum을 -비교할 수 있다. `L_e`는 Section NR-C01의 scale-aware element length와 일치시켜야 -한다. Physical `20 x 20` matrix에는 노드당 `(L_e I3, I2)` scaling을 적용한다. - -수치 rank, drilling-mode separation 및 condition evidence는 raw matrix가 아니라 이 -scaled matrix에서 정의해야 한다. Global `Kff`에도 model-level translational/rotational -scaling 계약이 필요하다. - -Rerun disposition: element `S20`, `S24`와 model-level `S_f`/`L_m`가 정의되었고, -rank/conditioning evidence는 `S^T K S`에서만 판정한다. 일관된 길이 단위 변환 시 -scaled stiffness가 공통 scalar만 얻는 것을 독립 차원 검산으로 확인했다. 실제 rank와 -condition threshold는 calibration evidence가 필요하다. - -### NR-C04 — Resolved — global 24-DOF weak form - -Formulation 7.1절은 +Let `R+` contain only the finite, strictly positive diagonal entries of the physical +local stiffness `K20` associated with the eight director-tangent rotational DOFs. +The formulation fixes ```text -delta epsilon_bar^{,T} C5 epsilon_bar +k_ref = min(R+) +k_d = 1e-3 * k_ref +K_drill_local = k_d * I4 +K_drill_24 = T_d^T * K_drill_local * T_d ``` -로 기록되어 있다. 쉼표는 미분 index가 아니며 의도한 식은 +All entries in `R+` have rotational-stiffness dimension `force*length`; translations, +off-diagonals, nonpositive values, and nonfinite values are excluded. Therefore +`k_d` has the correct dimension, `K_drill_24` is symmetric positive on the four pure +drilling coordinates, and the physical and drilling channels are algebraically +separate. An empty `R+` is a deterministic numerical-validation failure. This is a +complete algorithm contract, not a calibration placeholder. -$$ -\delta W_{int}^{phys} -=\int_{\Omega_0} -(\delta\overline{\boldsymbol\epsilon})^T -\mathbf C_5\overline{\boldsymbol\epsilon}\,dV -$$ +The deterministic nodal frames fix the local-coordinate representation, and +Formulation Section 5.3 supplies the virtual-work/energy congruence used by the +coordinate-transformation check. No unselected drilling coefficient or family +remains for Implementation Planning. -이다. 이후 `B^T C B` 식은 올바르므로 부호나 kernel 자체의 결함으로 전파되지는 -않는다. +#### 2.2 No drilling outputs — resolved and consistent -그러나 notation 오기 외에도 test-space mismatch가 있다. 물리 평형을 -`delta q20 in V20`에 대해 선언한 뒤 external work를 `delta qg^T f_CLOAD`로 쓰고, -drilling variation을 별도 절에 두었지만 하나의 complete 24-DOF weak form으로 -결합하지 않았다. Rectangular `T_p`를 사용하는 현재 계약에서는 다음과 같이 전역 -시험공간을 명시해야 한다. +Formulation Sections 7.2, 12.3, 12.5, 14, and 17.4 keep drilling out of physical +strain, resultant, stress, and reported physical shell energy. The internal identity +`E_drill = 0.5 gamma^T K_drill_local gamma` is permissible verification algebra; it +does not create an external result quantity. Requirements 035/036/046 and I/O +Sections 6.1/6.4/6.5 consistently require no drilling coefficient, stiffness, ratio, +or energy dataset. There is no output-contract defect. -$$ -\delta\mathbf q_g^T\left[ -\mathbf T_p^T\mathbf f_{int}^{20} -+\mathbf T_d^T\mathbf K_d^l\boldsymbol\gamma --\mathbf f_e^{CLOAD}\right]=0 -\qquad\forall\delta\mathbf q_g\in V_{24}^0, -$$ +#### 2.3 Exact B33 U/UR tolerance — resolved -$$ -\mathbf f_{int}^{20} -=\int_{\Omega_0}\overline{\mathbf B}^T -\mathbf C_5\overline{\mathbf B}\mathbf q_{20}\,dV. -$$ +For each case and component `c`, using only finite Abaqus rows, -동등하게 physical part만 쓸 때는 -`delta q20^T f_int20 = delta qg^T T_p^T f_int20`을 명시해야 한다. Element -equation은 이 global form과 일치하지만 weak-form source of truth가 다른 시험공간을 -혼용하므로 formulation revision이 필요하다. +```text +reference_scale_c = max(abs(reference_value_i)) +tolerance_c = 1e-9 + 1e-6 * reference_scale_c +``` -Rerun disposition: Section 7.1-7.2가 모든 `delta q_g in V24^0`에 대해 -`T_p^T f_int20 + T_d^T K_d gamma - f_CLOAD=0`을 선언하고 physical virtual-work -동등성을 함께 명시한다. transpose 오기도 제거되어 test-space mismatch가 해소되었다. +The `1e-9` floor is in the model's user-consistent length unit for `U1/U2/U3` and is +dimensionless for `UR1/UR2/UR3`. No row is zero-clamped and no row-specific relative +denominator replaces the component scale. `U1/U2/U3` exceedance is blocking at the +later Reference Verification gate; `UR1/UR2/UR3` uses the same formula but is +warning-only. The formula is exact and needs no MITC4-specific calibration. -### NR-C05 — Resolved at scope boundary — nonlinear coordinate mapping +#### 2.4 Removed and administrative items — nonblocking -Future section의 covariant Green-Lagrange first/second derivative와 +`NR-O03`, `NR-O04`, drilling sweeps, drilling-energy criteria, and expanded flat, +thin/thick, distorted, warped, curved-shell, or mesh-convergence portfolios are not +part of the approved implementation-planning gate. They may remain future research +or release evidence but shall not be reintroduced as missing numerical evidence. -$$ -K^{mat}_{AB}=\int B_A^T C_T B_B\,dV, -\qquad -K^{geo}_{AB}=\int s^T G_{AB}\,dV -$$ +Canonical reference naming, a bundle README, `metadata.json`, provenance, an Abaqus +version, duplicated units/coordinates/model/step/frame descriptions, or a schema +version are administrative information and cannot block this formulation verdict. +The absence of optional `metadata.json` is therefore not a defect. If such a file is +added later, it remains read-only context and cannot override the approved exact +paths, row mapping, or tolerance. -는 Total Lagrangian virtual work와 일관된다. 이는 -[[Total Lagrangian Shell Formulation]] 및 [[Green-Lagrange Strain Linearization]]과 -부합한다. +## Numerical Risk Assessment -그러나 nonlinear physical coordinate는 20개 director-chart coordinate로 정의된 -반면, linear limit에서 곧바로 `K_phys^24`로 환원된다고 서술한다. Finite rotation에서 -global `[URX,URY,URZ]`와 two-parameter director chart 사이의 mapping, 그 mapping의 -first/second derivative, chart update 및 objective drilling potential이 정의되지 않아 -이 환원은 현재 증명되지 않는다. - -이 finding은 승인 범위인 linear-static implementation을 차단하지 않지만, Section 15를 -미래 nonlinear implementation-ready formulation으로 사용할 수 없게 한다. 미래 -nonlinear gate 전에 별도 formulation revision이 필요하다. - -Rerun disposition: physical 20-coordinate residual/tangent와 조건부 global map -`q20=Phi(qg)`가 분리되었고, pullback tangent에 `A^T K20 A`뿐 아니라 residual-weighted -map Hessian 항이 포함되었다. scalar nonlinear map으로 재미분한 결과와 식이 -일치했다. 실제 `Phi`, chart update 및 objective drill potential은 future-only open -contract로 명시되어 현재 선형 구현 범위를 오염시키지 않는다. - -## 3. Confirmed Consistent Parts - -### 3.1 DOF ordering, director sign, and transformation - -- Global order `[UX,UY,UZ,URX,URY,URZ]`와 physical local order - `[uX,uY,uZ,alpha,beta]`는 요구조건과 일치한다. -- Right-handed `(a,b,d)`에서 - -$$ -\delta\mathbf d -=\boldsymbol\theta\times\mathbf d -=-\alpha\mathbf b+\beta\mathbf a -$$ - - 이므로 rotation sign은 원 MITC4 문헌과 일치한다. -- `T_p=P T`, `T_d=D_gamma T`의 크기는 각각 `20 x 24`, `4 x 24`이며 - virtual work를 보존한다. -- Orthonormal frame과 disjoint selector 때문에 - -$$ -\mathbf T_p\mathbf T_d^T=\mathbf0. -$$ - - 따라서 `rank(K20)=14`, `k_d,I>0`을 전제로 physical rank 14와 drill rank 4가 - 서로 중첩되지 않아 exact-arithmetic stabilized rank는 18, nullity는 6이다. -- Physical rigid mode에서 - -$$ -\boldsymbol\theta_I -=\boldsymbol\omega-(\boldsymbol\omega\cdot\mathbf d_I)\mathbf d_I -$$ - - 로 `gamma=0`을 구성하는 규약은 approved five-DOF gauge contract와 일치한다. - -수치적으로 이 rank를 판정하는 방법은 NR-C03 수정과 drilling calibration 이후에만 -승인할 수 있다. - -### 3.2 MITC tying and B operator - -Tying alias를 원 논문의 A/B/C/D로 다시 쓰면 - -| FESA location | source alias | component | +| risk | current assessment | required in-scope control | | --- | --- | --- | -| `T_xi+ = (0,+1,0)` | A | `epsilon_xi-zeta` | -| `T_xi- = (0,-1,0)` | C | `epsilon_xi-zeta` | -| `T_eta+ = (+1,0,0)` | D | `epsilon_eta-zeta` | -| `T_eta- = (-1,0,0)` | B | `epsilon_eta-zeta` | - -이므로 interpolation weight와 edge inventory는 원 MITC4 식과 일치한다. -Direct covariant strain column - -$$ -B^{DI}_{\alpha\beta,A} -=\frac12(\mathbf G_\alpha\cdot\mathbf h_{A,\beta} -+\mathbf G_\beta\cdot\mathbf h_{A,\alpha}) -$$ - -도 small-strain covariant relation과 일치한다. Tied covariant tensor를 reciprocal -basis로 복원하고 engineering shear factor를 적용하는 순서가 명확하며, residual과 -stiffness가 같은 projection을 사용한다. 이는 [[Assumed Transverse Shear Strain -Interpolation]]의 핵심 consistency 요구를 만족한다. - -### 3.3 Constitutive matrix and units - -- `Cps`의 engineering `gamma12` coefficient는 `G`이고 transverse shear block은 - `(5/6)G I2`다. -- `-1 < nu < 0.5`, `E>0`에서 `C5`는 symmetric positive definite다. -- `sigma33=0`, thickness strain 제외, centered homogeneous layer boundary가 - 요구조건과 일치한다. -- `K20`, force, resultant, curvature 및 energy의 차원은 다음과 같이 일관된다. - -| quantity | units | -| --- | --- | -| membrane/shear strain | `1` | -| curvature | `1/length` | -| `N`, `Q` | `force/length` | -| `M` | `force` | -| physical/drilling energy | `force*length` | - -`5/6`은 승인된 homogeneous rectangular-thickness 범위에만 사용하므로 범위 확장도 -없다. - -### 3.4 Integration and hourglass assessment - -- `xi,eta,zeta = +/-1/sqrt(3)`, 모든 weight `1`인 `2 x 2 x 2` 규칙은 원 elastic - MITC4의 `2 x 2` midsurface와 두 thickness point 근거에 부합한다. -- Tying shear는 midsurface edge 값으로부터 만들어 두 thickness point에서 공통으로 - 사용하며, 나머지 mapping과 in-plane strain은 실제 thickness point에서 평가한다. -- `S4`와 `S4R`이 동일한 full-integration path를 사용한다는 product mapping이 - 명확하다. -- `1 x 1` reduced integration이 없으므로 별도 hourglass control은 `N/A`다. - -이는 [[MITC4 Shell Element]]의 full `B^T D B` 경로 및 원 문헌의 no-spurious-mode -관찰과 일치한다. 다만 실제 rank는 distortion 및 drilling scaling을 포함한 test로 -확인해야 한다. - -### 3.5 Recovery signs and locations - -정의 - -$$ -\boldsymbol\epsilon_0=\frac1t\int\mathbf e_m\,dz, -\qquad -\boldsymbol\kappa=\frac{12}{t^3}\int z\mathbf e_m\,dz -$$ - -로부터 `e_m(z)=epsilon0+z kappa`이면 정확히 원래 `epsilon0`, `kappa`를 복구한다. -동일한 fixed midsurface local frame과 동일한 thickness quadrature를 사용하므로 - -$$ -\mathbf N=\mathbf A\boldsymbol\epsilon_0, -\qquad -\mathbf M=\mathbf D\boldsymbol\kappa, -\qquad -\mathbf Q=\mathbf A_s\boldsymbol\gamma_0 -$$ - -가 centered homogeneous layer에서 일관된다. Bottom `z=-t/2`, top `z=+t/2`, -`M=integral(z sigma dz)`의 부호도 서로 모순되지 않는다. Output order와 위치는 -요구조건과 일치한다. - -### 3.6 Linear reaction and equilibrium sign - -Full residual을 `r=K d-F`로 정의했으므로 constrained component는 반력이고 free -component는 equilibrium evidence다. 전역 force/moment balance에서 applied load와 -reaction을 더해 zero를 확인하는 부호도 이 정의와 일치한다. - -## 4. Numerical Decisions - -### 4.1 Approved in this review - -#### NR-D01 — Drilling-direction nodal moment projection - -Nonzero nodal moment에 대해 - -$$ -\rho_M=\frac{|\mathbf d_I\cdot\mathbf M_I|}{\|\mathbf M_I\|} -$$ - -를 사용하고 `rho_M <= 1e-12`인 경우에만 tangent-plane moment로 수용한다. Zero moment는 -별도 exact-zero case로 수용하며 denominator를 clamp하지 않는다. 이 기준은 -`FESA-REQ-LSMITC4-051`의 normalized frame/orthogonality 기준과 일치하고 길이/힘 -단위에 불변이다. - -#### NR-D02 — Algebraic normalized checks - -Formulation revision에서 다음 normalization을 명시한다. - -$$ -e_{sym}=\frac{\|\widehat K-\widehat K^T\|_F}{\|\widehat K\|_F} -\le10^{-12}, -$$ - -$$ -e_{rigid}=\frac{\|\widehat K\widehat r\|_2} -{\|\widehat K\|_2\|\widehat r\|_2}\le10^{-10}, -$$ - -$$ -e_{frame}=\|R^TR-I\|_F\le10^{-12}. -$$ - -Zero matrix/vector denominator는 pass로 clamp하지 않고 invalid test construction으로 -분류한다. Transformation-energy check는 nonzero reference energy에 대해 - -$$ -e_T=\frac{|E_g-E_l|}{|E_g|+|E_l|}\le10^{-12} -$$ - -를 적용하며 양쪽 energy가 exact zero인 rigid/pure-null case는 별도 action test로 -판정한다. - -### 4.2 Open decisions — blocking evidence gaps - -#### NR-O01 — Open — Drilling reference family, nominal coefficient, and plateau - -NR-C02/NR-C03을 반영한 normalized sweep 결과가 없으므로 후보 A/B/physical-block -중 어느 것도 승인하지 않는다. Exact-arithmetic positivity만으로 practical -factorization과 physical contamination을 동시에 보장할 수 없다. - -#### NR-O02 — Open — Drilling energy warning ratio - -Source는 static drill-specific acceptable ratio를 제공하지 않는다. Nominal plateau에서 -`U/N/M/Q` 민감도와 함께 calibrate해야 하며, 현 단계에서 `1%`, `5%` 등의 임의 값을 -승인하지 않는다. `Ephys`가 zero/near-zero이면 ratio를 만들지 않고 두 energy와 case -classification을 보고하는 formulation 원칙은 승인한다. - -#### NR-O03 — Open — Smooth-director angle - -`20 degrees`는 usable initial candidate이나 Abaqus grouping heuristic을 FESA hard -rejection으로 바꾸는 결정이다. 현재 S4/S4R artifact는 모두 평면이어서 -incident-normal deviation이 이 경계를 시험하지 않는다. Pinched cylinder와 LE3의 -coarse-to-fine mesh에서 incident normal deviation 분포와 -false-fold/false-smoothing case를 확인하기 전에는 승인하지 않는다. - -#### NR-O04 — Open — Geometry thresholds - -NR-C01의 measure inventory는 고정되었다. 현재 artifact는 평면 정규 mesh의 -한 점만 제공하므로 threshold 근거가 아니다. Valid distortion/warp sweep과 -collapsed/inverted negative sequence가 pass/fail 사이에 분리 영역을 제공해야 -threshold를 승인할 수 있다. - -#### NR-O05 — Partially resolved — U tolerance and UR warning threshold - -이 값은 Reference Model과 공동 소유이다. 현재 artifact로 S4/S4R 각 49개 -U/UR node row와 component scale은 관찰할 수 있어 presence 부분은 해소되었다. -그러나 unit label, approved provenance, mesh/convergence uncertainty, tolerance proposal가 -없으므로 수치값은 승인하지 않는다. U-only blocking, UR warning-only 정책만 -유지한다. - -### 4.3 Read-only reference artifact re-inspection - -두 bundle은 수정 없이 다음과 같이 관찰되었다. - -| model candidate | input identity | observed result inventory | numerical relevance | contract status | -| --- | --- | --- | --- | --- | -| `reference/shell/` | `shell.inp`, SHA-256 `4005851E1AB22FD3A16AC17A8D5DA3E051233F69F37419079F3553AD134ECFCF`, `TYPE=S4` | displacement 49 rows, reaction 49 rows, stress 288 rows | S4 source presence and one regular flat-plate U/UR scale | I/O-approved S4 legacy alias, but feature Reference Model Contract and bundle README are absent | -| `reference/shellR/` | `shellR.inp`, SHA-256 `1325940FB42B78961CF25E84379BF2693846FAD22473E7688AC5456B37B18CB4`, `TYPE=S4R` | displacement 49 rows, reaction 49 rows, stress 288 rows | S4R source presence and paired same-model U/UR scale | observed noncanonical bundle; no approved canonical/legacy-alias disposition and no bundle README | - -`shell.inp` and `shellR.inp`는 job name과 source `TYPE`만 다르다. 두 모델은 -49 nodes, 36 elements의 평면 정규 `6 x 6` mesh, `t=0.5`, `E=2.1e11`, -`nu=0.3`, 중앙 절점 `-100000` global-Z CLOAD와 전체 둘레 6-DOF 구속을 -공유한다. 중앙 절점 `U3`는 S4 `-2.37408203e-5`, S4R -`-2.45598239e-5`이다. 각 displacement/reaction CSV의 node key는 49개이며 -중복이 없고 수치값은 유한하다. - -이 inventory는 새로 중요한 정보이지만 calibration portfolio는 아니다. 두 -deck은 단일 두께의 regular planar case이므로 shear/membrane locking trend, -distortion/warp rejection, curved director angle, drilling plateau 및 mesh convergence를 -판정할 수 없다. S4/S4R Abaqus 차이는 두 Abaqus formulation이 다름을 보여줄 -뿐 FESA drilling/geometry 상수를 선택하지 않는다. - -두 bundle 모두 `metadata.json`이 없다. 이는 project-wide 정책상 -`absent-allowed`이며 불완전 판정 근거가 아니다. 다만 선택 JSON의 부재가 -Reference Model Contract이 소유해야 할 provenance, units, coordinate system, -step/frame, schema, tolerance를 없애지는 않는다. 현재는 그 contract 자체가 -없으며, 일반 bundle 정책이 요구하는 `README.md`도 두 경로 모두에 없다. -`metadata.json` 부재와 이 두 필수 계약 공백은 서로 구분한다. 따라서 현재 두 -bundle은 numerical acceptance evidence로 사용할 수 없다. - -## 5. Numerical Risk Assessment - -| risk | assessment | status/control | -| --- | --- | --- | -| rigid body modes | 물리 20-DOF rank 14와 4 drill mode의 algebraic 분리는 타당 | scaled spectrum과 explicit six mode test 필요 | -| patch test | membrane, bending, shear, twist field 정의가 가능 | 구현 전 component/sign별 exact field test 필요 | -| symmetry | `B^T C B`, orthogonal congruence, diagonal drill로 구조상 symmetric | NR-D02 normalized check 적용 | -| positive definiteness | free element는 six-mode semidefinite, valid constrained `Kff`는 positive definite 기대 | geometry/drill calibration 뒤 확인 | -| hourglass | full `2 x 2` midsurface integration | `N/A`; spurious-mode eigencheck는 유지 | -| shear locking | MITC tying으로 목표 현상을 완화 | thickness/mesh sequence 없이는 통과 주장 금지 | -| membrane locking | original MITC4의 distorted curved-shell known limitation | curved/distorted convergence와 known limitation 기록 | -| volumetric locking | approved plane-stress shell 범위 | `N/A`; 3D incompressible 의미로 확장 금지 | -| distortion | measure inventory는 완전하나 calibrated threshold 없음 | geometry calibration evidence 필요 | -| singular Jacobian | sign/scale-aware measures 고정, near-singular threshold 미승인 | valid/invalid separation sweep 필요 | -| conditioning | scaled matrix 계약은 타당하나 drilling nominal point 미승인 | normalized sweep과 factorization evidence 필요 | -| linear solve convergence | direct linear solve에서는 Newton convergence N/A | residual/equilibrium `1e-10` 확인 | -| mesh convergence | shear/membrane locking 및 curved response에 필수 | pinched cylinder/LE3 sequence 필요 | -| nonlinear tangent | 물리 20-DOF 및 conditional global-map variation 구조는 타당 | actual chart/update 미정으로 future implementation blocked | - -## 6. Consistency Checks - -| check | result | evidence/comment | -| --- | --- | --- | -| material/section units | pass | `E, G, t`, `A/D/As`와 output units 일치 | -| drilling dimensions | pass | 모든 후보와 `Kd`는 `force*length` | -| rank/conditioning dimensional invariance | pass at contract level | `S20/S24/Sf`와 `S^T K S` 정의; 수치 threshold evidence는 미제출 | -| rotation/director signs | pass | `delta d=-alpha b+beta a` | -| tying signs and inventory | pass | A/C/D/B alias와 weight 일치 | -| DOF ordering | pass | global 6, physical 5 per node 정확 | -| coordinate transforms | pass for linear scope | linear `T_p/T_d` 타당; future map은 명시적 conditional contract | -| matrix/vector dimensions | pass | 20/24/4 block 크기 일치 | -| constitutive symmetry/positivity | pass | approved `E,nu` 범위 | -| integration points/weights | pass | `2 x 2 x 2`, weight 1 | -| Jacobian near-singularity contract | pass at measure level | `a_g`가 orthogonal collapse를 검출; threshold calibration은 미제출 | -| stiffness/residual sign | pass | `r=Kd-F`, reaction/equilibrium 일치 | -| output component order | pass | generalized/resultant/stress order 일치 | -| output locations | pass | four midsurface points와 bottom/mid/top 분리 | -| weak-form test space/notation | pass | complete global 24-DOF variation과 physical virtual-work equivalence | -| future material/geometric tangent | pass at documented boundary | 20-DOF tangent와 map Hessian 포함; actual chart/update는 future-only | - -## 7. Verification Readiness - -- unit_tests: Section 7.1의 algebraic, frame, tying, rank, energy 및 geometry tests. -- patch_tests: Section 7.2의 membrane, bending, shear, twist 및 rigid/drill states. -- mms_or_mes: CLOAD-only 범위에서는 prescribed polynomial element state를 이용한 - manufactured element solution을 사용하며 distributed-load full-domain MMS는 `N/A`다. -- benchmark_reference_comparison: Section 7.3의 pinched cylinder, LE3 및 승인된 - S4/S4R displacement evidence. 현재 평면 정규 쌍은 source-type presence 자료이며 - 단독 benchmark portfolio로는 불충분하다. -- missing_evidence: Section 7.5의 drilling, geometry, director-angle, reference 및 - future nonlinear evidence. - -### 7.1 Unit and algebraic tests required - -1. Shape partition, Kronecker delta, derivative sum. -2. Nodal/integration frame orthonormality, handedness, deterministic tie break. -3. `T_p T_d^T=0`, virtual work 및 energy congruence. -4. Source A/C/D/B tying value를 독립 hand calculation과 비교. -5. `K20`, `Kphys`, `Kdrill`, `Ke` symmetry와 separate energy. -6. Six physical rigid vectors, four pure drill vectors, scaled spectrum/rank. -7. Force/length 단위 변경 후 `K_hat`, rank decision, displacement/resultant invariance. -8. NR-C01 직교 collapse sequence와 inverted/warped/opposed-normal negative cases. -9. Bottom/mid/top stress와 thickness moment recovery의 analytical cross-check. -10. S4/S4R source type만 바꾼 동일 model의 internal-row equality. - -### 7.2 Patch and manufactured element states - -- constant `E11`, `E22`, `G12` membrane states; -- `K11`, `K22` pure bending과 top/bottom stress reversal; -- `K12` pure twist; -- `G13`, `G23` constant transverse shear; -- physical rigid motion과 pure drilling separation. - -Distributed load가 없어도 prescribed nodal field와 element action으로 patch algebra를 -검증할 수 있다. 각 test는 component order와 sign을 별도로 판정해야 한다. - -### 7.3 Locking and benchmark evidence required - -- thin/thick cantilever 또는 plate의 thickness 및 mesh sequence; -- regular/distorted pinched cylinder sequence; -- NAFEMS LE3 coarse-to-fine sequence와 incident-normal angle inventory; -- 필요 시 equivalent nodal loads를 명시한 Scordelis-Lo 보조 sequence; -- S4 및 S4R source artifact 각 하나 이상. 현재 두 regular-flat artifact는 - presence를 닫지만 thin/thick/distorted/curved coverage를 대체하지 않는다. - -[[Shell Locking Phenomenon]]에 따라 한 개 mesh의 displacement 일치만으로 locking -absence를 주장하지 않는다. [[MITC4 Shell Element]]의 patch 및 Scordelis-Lo 근거는 -element family의 타당성을 지지하지만 FESA의 director/drilling/output convention을 -자동 검증하지 않는다. - -### 7.4 Drilling calibration evidence required - -NR-C02의 `rho_d`를 사용해 다음 두 실패 경계를 모두 포착해야 한다. - -- low side: scaled positive spectrum이 solver rank threshold 아래로 내려가거나 - `Kff` conditioning/factorization이 불안정해지는 지점; -- high side: U 또는 physical `N/M/Q`가 인접 decade에서 승인된 contamination bound를 - 넘거나 drilling energy가 physical response를 지배하는 지점. - -Stable interval이 존재하지 않으면 선택한 diagonal absolute-drill 방법 자체를 -Requirements/Formulation으로 되돌려 재검토해야 한다. - -### 7.5 Missing evidence - -- dimensionally normalized drilling sweep 결과; -- fixed geometry metric의 valid/invalid separation data; -- curved benchmark별 incident-normal angle distribution; -- approved MITC4 Reference Model Contract; -- S4R noncanonical bundle의 승인된 canonical/legacy-alias disposition; -- 두 bundle의 required `README.md` 처리; -- reference provenance, units, coordinate system, step/frame, schema, tolerance; -- U mixed tolerance와 UR warning threshold의 mesh/convergence 근거. - -S4/S4R artifact presence와 raw U/UR component scale 관찰은 더 이상 missing이 아니다. -`metadata.json`도 missing evidence가 아니며 부재를 `absent-allowed`로 기록한다. - -Future nonlinear chart/update 및 objective drilling evidence도 아직 없지만 현재 linear -gate의 dependency는 아니다. 이를 근거로 기하비선형 구현을 시작해서는 안 된다. - -### 7.6 Gate matrix - -| gate item | result | consequence | -| --- | --- | --- | -| current-linear formulation consistency | pass | 추가 formulation revision 불필요 | -| `NR-C01`-`NR-C05` disposition | resolved | 1차 confirmed defect 종료 | -| `NR-D01`-`NR-D02` integration | pass | 수식/normalized metric 유지 | -| `NR-O01`-`NR-O04` drilling/geometry/director calibration | open | Implementation Planning 차단 | -| S4/S4R artifact presence | resolved | 두 source type의 read-only bundle 존재 확인 | -| `NR-O05` U/UR scale observation | partially resolved | raw rows/scales는 존재하나 threshold 승인 불가 | -| reference model contract and artifact usability | open | primary verdict `needs-reference-model` | -| optional `metadata.json` absence | resolved | `absent-allowed`; gate 차단 아님 | -| future geometric-nonlinear executability | out of current scope | 별도 future formulation/review 전 구현 금지 | - -## 8. Required Revisions +| Transverse-shear locking | controlled for the original MITC4 scope, not claimed eliminated for every mesh | Use the exact edge-midpoint covariant shear projection of Sections 10.2-10.4 and pass transverse-shear patch/reference checks. | +| Curved/distorted-mesh membrane locking | known limitation of the original MITC4 family | Preserve the documented limitation. An expanded convergence portfolio is nonblocking and does not authorize MITC4+. | +| Volumetric locking | not applicable to the approved plane-stress shell contract | Do not reinterpret `C5` as a full 3D nearly incompressible material law. | +| Hourglass modes | no reduced-integration/hourglass path is approved | Both source `S4` and `S4R` use the same full `2x2x2` FESA integration and MITC tying path. | +| Degenerate, inverted, or self-intersecting geometry | fail-closed contract is present | Enforce distinct connectivity, non-self-intersection, finite nonzero surface measure, finite reciprocal bases, and `J>0` at every required location. | +| Near-singular but still positive geometry | conditioning may degrade because no calibrated quality threshold is in scope | Preserve finite checks and deterministic solver failure diagnostics; do not invent `NR-O04` thresholds. | +| Opposed or invalid nodal directors | would corrupt frames, signs, and tying | Reject nonfinite/zero candidates, nonpositive incident-normal agreement, and nonfinite/zero averages; use duplicate source nodes for folds. | +| Drilling singularity | four nonphysical modes would remain without regularization | Apply the exact fixed `R+` rule and verify stabilized nullity six. | +| Drilling contamination of physics | possible if drill enters the physical operator or recovery | Keep `T_p` and `T_d` separate and verify pure drill has zero physical strain/resultant/stress and no physical energy contribution. | +| Rigid-mode test contamination | a full spatial rotation vector can contain director-parallel rotation | Construct physical rigid rotation with `u_I=omega x X_I`, `delta d_I=omega x d_I`, and `gamma_I=0` as specified in Section 8.3. | +| Wrong shear component/factor | would cause patch failure or incorrect shear energy | Keep the `xi-zeta`/`eta-zeta` tying pairs and engineering factor `gamma_ij=2 epsilon_ij` explicit. | +| Recovery sign/location drift | could hide a correct stiffness behind wrong outputs | Reuse stiffness frames, tying, material, and thickness quadrature; preserve four Gauss identities and bottom/middle/top positions without averaging. | +| Future nonlinear misuse | current Section 15 does not define a complete global nonlinear element | Keep it non-executable until a separate approved nonlinear formulation closes `Phi`, map curvature, objective drill, load work, and state. | + +## Consistency Checks + +### 1. DOF order, director sign, and coordinate transforms — pass + +- Global order is exactly `[UX,UY,UZ,URX,URY,URZ]` per node. +- `R_I=[a_I b_I d_I]` is right-handed and orthonormal, with + `[alpha,beta,gamma]^T=R_I^T theta_I^g`. +- The director variation `delta d_I=beta_I a_I-alpha_I b_I` has the correct sign for + `theta_I x d_I`. +- `T_p` is `20x24`; `T_d` is `4x24`. The physical operator receives only `q20`, and + the drilling potential receives only `gamma`. +- The transpose maps in Formulation Sections 5.3 and 7.2 preserve virtual work and + energy in the common 24-DOF space. + +### 2. Shape functions, geometry, and B operator — pass + +- The bilinear shape functions satisfy partition of unity, nodal interpolation, and + derivative-sum identities. +- The degenerated geometry uses a dimensionless unit director and separate thickness + factor `t*zeta/2`, avoiding thickness double-counting. +- The direct covariant strain column is the symmetric gradient written in covariant + bases. The two transverse covariant shear components alone are replaced by the + canonical MITC4 edge-midpoint interpolation. +- Reconstructing with reciprocal bases before local projection preserves the tensor + meaning. Engineering shear factors are applied once in the local five-component + vector. +- The same projected `B_bar` is used in strain, residual, stiffness, and recovery; + no direct/tied shear mismatch remains. + +### 3. Constitutive matrix and dimensional consistency — pass + +- For finite `E>0` and `-1 GREEN -> VERIFY` 순서로 변환한다. -- Future nonlinear state/tangent는 현재 linear implementation plan에 포함하지 않는다. +Implementation Planning is authorized. The plan shall: + +- cover the deterministic director/frame preprocessing, `24 -> 20 + 4` transforms, + covariant MITC tying, full `2x2x2` integration, fixed drilling split, and recovery; +- trace every approved must-requirement to TDD tests, including the invariant, patch, + fixed-drilling, failure, schema, row-matching, and U/UR decision behaviors above; +- preserve one internal `FESA-MITC4` numerical path for source S4 and S4R while keeping + source metadata distinct; +- keep drilling out of physical recovery and HDF5 results; +- exclude future nonlinear execution, calibration sweeps, removed `NR-O03/NR-O04`, + expanded portfolios, and administrative reference requirements. + +This handoff authorizes planning only. It does not authorize Harness execution, +production-code changes, reference-artifact mutation, or a claim of implementation +completion. ### I/O Definition Agent -- 현재 I/O definition은 이 rerun의 reviewed input이지만 Numerical Review 통과를 - 의미하지 않는다. Geometry threshold, drilling coefficient/energy warning, - U/UR tolerance를 implementation default로 선점하지 않는다. -- Section 7.3의 “S4R bundle missing” 서술은 현재 물리 inventory와 다르다. - 다만 `reference/shellR/`의 noncanonical naming과 contract 부재 때문에 “usable - canonical S4R evidence missing” dependency는 남는다. 이 구분을 다음 I/O 메타데이터 - refresh에 반영한다. -- NR-D01의 normalized drilling-load projection과 exact-zero handling을 diagnostic - contract에 반영한다. +The current I/O contract is numerically consistent with the formulation. Planning +shall preserve its exact source identity, load projection, output units/locations, +physical-energy meaning, reference row mapping, and U/UR decision rule. -### Reference Model Agent +### Reference Verification and Physics Evaluation Agents -- Section 4.3/8의 read-only inventory를 계약으로 승인하고 누락 benchmark - evidence를 준비한다. -- Abaqus S4/S4R formulation equivalence를 주장하지 않고 global U만 blocking evidence로 - 사용한다. +These remain downstream of implementation and build/test. Reference Verification +will decide U/UR comparison outcomes; Physics Evaluation will independently assess +equilibrium, signs, symmetry, and physical plausibility. Neither result is asserted +by this review. -### Coordinator Agent +## Review Evidence -- Formulation revision loop는 종료한다. -- `needs-numerical-calibration`과 `needs-reference-model`을 남은 dependency로 추적한다. -- 두 dependency가 닫히고 Numerical Review가 재승인하기 전에 다음 formal gate를 열지 - 않는다. - -## 10. Evidence - -### Repository sources - -- `docs/formulations/mitc4-shell-formulation.md` -- `docs/research/linear-static-mitc4-shell-research.md` -- `docs/requirements/linear-static-mitc4-shell.md` -- `docs/io-definitions/linear-static-mitc4-shell-io.md` -- `docs/reference-models/README.md` -- `reference/shell/` S4 input/displacement/reaction/stress bundle (read-only) -- `reference/shellR/` S4R input/displacement/reaction/stress bundle (read-only) -- `docs/reference-papers/MITC4/AContinuumMechanicsBasedFourNodeShell/` -- `docs/reference-papers/MITC4/FourNodeQuadrilateralShellElementMITC4/` -- `docs/reference-papers/MITC4/유한요소해석법을이용한쉘구조물의동적좌굴해석/` - -### FEM wiki cross-checks - -- [[MITC4 Shell Element]] — physical five-DOF kinematics, edge-midpoint tying, - `B^T D B`, patch 및 convergence evidence. -- [[MITC Shell Kinematics]] — midsurface/director/thickness mapping. -- [[Assumed Transverse Shear Strain Interpolation]] — shear-locking remedy와 projection - consistency. -- [[Shell Locking Phenomenon]] — transverse-shear 및 curved-shell membrane locking 구분. -- [[Total Lagrangian Shell Formulation]] — reference-configuration residual/tangent. -- [[Green-Lagrange Strain Linearization]] — material/geometric tangent 분리. - -Wiki는 교차 확인 근거이며 최종 project authority는 approved requirements, research 및 -reviewed formulation이다. +This review used the repository policy/design files, the approved requirements, +research, formulation, I/O definition and reference-case inventory listed in +Metadata, plus read-only inspection of the four declared artifacts. Local FEM wiki +material cross-checked MITC4 kinematics, edge-midpoint assumed shear and known locking +risks; the approved repository documents remain the feature source of truth. diff --git a/docs/reference-models/linear-static-mitc4-shell-reference-models.md b/docs/reference-models/linear-static-mitc4-shell-reference-models.md index c233de4..ba2c0a6 100644 --- a/docs/reference-models/linear-static-mitc4-shell-reference-models.md +++ b/docs/reference-models/linear-static-mitc4-shell-reference-models.md @@ -5,7 +5,7 @@ - feature_id: `linear-static-mitc4-shell` - source_requirement: `docs/requirements/linear-static-mitc4-shell.md` - source_io_definition: `docs/io-definitions/linear-static-mitc4-shell-io.md` -- status: `approved-ready-for-numerical-review` +- status: `approved-for-implementation-planning` - owner_agent: `reference-model-agent` - date: `2026-08-12` - artifact_policy: `read-only-existing-files` @@ -117,5 +117,5 @@ before Implementation Planning or feature completion. Numerical Review may use this inventory as downstream comparison input, but missing bundle-administration data shall not change a mathematically consistent formulation -verdict. Implementation Planning remains unauthorized until the revised Numerical -Review explicitly passes the formulation for planning. +verdict. The revised Numerical Review passes the formulation and authorizes +Implementation Planning; this does not authorize implementation or Harness execution.