# Step 3: MITC4 Kinematics and Constitutive Law

## 담당 역할과 필수 스킬

- 담당 역할: `implementation-agent`
- 필수 스킬: `harness`, `fesa-cpp-msvc-tdd`

## 읽어야 할 파일

- `/.agents/skills/harness/SKILL.md`, `/.codex/skills/fesa-cpp-msvc-tdd/SKILL.md`
- `/AGENTS.md`, `/docs/PRD.md`, `/docs/ARCHITECTURE.md`, `/docs/ADR.md`
- `/docs/HARNESS.md`, `/docs/HARNESS_WORKFLOW.md`, `/.codex/hooks.json`
- `/docs/linear-static-mitc4-shell/implementation-plan.md`
- `/docs/linear-static-mitc4-shell/requirements.md` Requirements 031-038/050-052
- `/docs/linear-static-mitc4-shell/research.md`
- `/docs/linear-static-mitc4-shell/formulation.md` Sections 3-11, 17
- `/docs/linear-static-mitc4-shell/numerical-review.md` Sections 5.1-5.6, 6.1-6.2
- `/docs/linear-static-mitc4-shell/io.md`
- `/docs/linear-static-mitc4-shell/reference-model.md`
- phase indexes, `step3.md`, Step 2 geometry paths/summary
- `/include/fesa/elements/euler_beam_3d.hpp`와 cpp는 concrete value-kernel style 참고용
- Candidate new `/include/fesa/elements/mitc4_shell.hpp`
- Candidate new `/src/fesa/elements/mitc4_shell.cpp`
- Candidate new `/tests/unit/elements/mitc4_shell_test.cpp`
- source/test CMakeLists

## 작업

1. `MITC4-KIN-001..005` tests를 먼저 작성한다.
2. Public common Element hierarchy 없이 concrete `Mitc4Shell` value type을 만든다.
3. Candidate creation seam은 four nodes, four initial directors, `ShellSection`,
   `LinearElasticMaterial`을 받아 validated `Result<Mitc4Shell>`을 반환한다.
4. Shape/derivative identities, local frames, `T_p`/`T_d` channel maps, direct
   membrane/bending columns, four covariant MITC edge-midpoint tying samples와
   interpolation weights, engineering shear factors를 구현한다.
5. `C_ps`, `C_5`, `A`, `D`, `A_s`의 exact coefficients, dimensions, symmetry,
   positive definiteness와 unit rescaling을 구현한다.
6. `2x2x2` Gauss point/weight order를 고정하고 intermediate physical matrices는
   20 DOF contract를 유지한다.

## Acceptance Criteria

```powershell
$requiredBuildPaths=@("C:/git/googletest","C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl","C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb","C:/Program Files/HDF_Group/HDF5/2.1.1/cmake")
foreach($p in $requiredBuildPaths){if(-not(Test-Path -LiteralPath $p)){throw "Missing $p"}}
cmake --fresh -S . -B .harness/build -G "Visual Studio 18 2026" -A x64 `
  "-DFESA_GTEST_SOURCE_DIR=C:/git/googletest" `
  "-DMKL_DIR=C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl" `
  "-DTBB_DIR=C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb" `
  "-DHDF5_DIR=C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"
cmake --build .harness/build --config Debug --target fesa_unit_tests
ctest --test-dir .harness/build -C Debug -R "Mitc4ShellKinematics|Mitc4ShellConstitutive" --output-on-failure
```

Expected missing kernel/kinematics RED를 기록한 뒤 minimal GREEN. 이후:

```powershell
cmake --build .harness/build --config Debug --target fesa_unit_tests
ctest --test-dir .harness/build -C Debug -R "Mitc4ShellKinematics|Mitc4ShellConstitutive|Mitc4Geometry" --output-on-failure
cmake --build .harness/build --config Debug
ctest --test-dir .harness/build -C Debug --show-only=json-v1
ctest --test-dir .harness/build -C Debug --output-on-failure
```

## 검증 및 상태 갱신

현재 Step의 RED와 focused/full evidence만 기록하고 상태 payload만 갱신한다.

## 금지사항

- Global assembly, drilling stiffness, recovery/HDF5를 구현하지 마라.
- S4R source type으로 quadrature를 분기하지 마라.
- Nonlinear state/residual/tangent를 구현하지 마라.
- Vendor type을 public header에 노출하거나 직접 commit/hook 실행을 하지 마라.
