feat(hydrotech-beam): Phase 1 LHS DoE study code

Implements the optimization study code for Phase 1 (LHS DoE) of the
Hydrotech Beam structural optimization.

Files added:
- run_doe.py: Main entry point — Optuna study with SQLite persistence,
  Deb's feasibility rules, CSV/JSON export, Phase 1→2 gate check
- sampling.py: 50-point LHS via scipy.stats.qmc with stratified integer
  sampling ensuring all 11 hole_count levels (5-15) are covered
- geometric_checks.py: Pre-flight feasibility filter — hole overlap
  (corrected formula: span/(n-1) - d ≥ 30mm) and web clearance checks
- nx_interface.py: NX automation module with stub solver for development
  and NXOpen template for Windows/dalidou integration
- requirements.txt: optuna, scipy, numpy, pandas

Key design decisions:
- Baseline enqueued as Trial 0 (LAC lesson)
- All 4 DV expression names from binary introspection (exact spelling)
- Pre-flight geometric filter saves compute and prevents NX crashes
- No surrogates (LAC lesson: direct FEA via TPE beats surrogate+L-BFGS)
- SQLite persistence enables resume after interruption

Tested end-to-end with stub solver: 51 trials, 12 geometric rejects,
39 solved, correct CSV/JSON output.

Ref: OPTIMIZATION_STRATEGY.md, auditor review 2026-02-10

projects/hydrotech-beam/studies/01_doe_landscape/geometric_checks.py

@@ -0,0 +1,205 @@
+"""Geometric feasibility pre-flight checks for Hydrotech Beam.
+
+Validates trial design variable combinations against physical geometry
+constraints BEFORE sending to NX. Catches infeasible combos that would
+cause NX rebuild failures or physically impossible geometries.
+
+References:
+    OPTIMIZATION_STRATEGY.md §4.2 — Hole overlap analysis
+    Auditor review 2026-02-10 — Corrected spacing formula
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import NamedTuple
+
+
+# ---------------------------------------------------------------------------
+# Fixed geometry constants (from NX introspection — CONTEXT.md)
+# ---------------------------------------------------------------------------
+BEAM_HALF_HEIGHT: float = 250.0  # mm — fixed, expression `beam_half_height`
+HOLE_SPAN: float = 4000.0  # mm — expression `p6`, total distribution length
+MIN_LIGAMENT: float = 30.0  # mm — minimum material between holes (mesh + structural)
+
+
+class FeasibilityResult(NamedTuple):
+    """Result of a geometric feasibility check."""
+
+    feasible: bool
+    reason: str
+    ligament: float  # mm — material between adjacent holes
+    web_clearance: float  # mm — clearance between hole edge and faces
+
+
+@dataclass(frozen=True)
+class DesignPoint:
+    """A single design variable combination."""
+
+    beam_half_core_thickness: float  # mm — DV1
+    beam_face_thickness: float  # mm — DV2
+    holes_diameter: float  # mm — DV3
+    hole_count: int  # — DV4
+
+
+def compute_ligament(holes_diameter: float, hole_count: int) -> float:
+    """Compute ligament width (material between adjacent holes).
+
+    The NX pattern places `n` holes across `hole_span` mm using `n-1`
+    intervals (holes at both endpoints of the span).
+
+    Formula (corrected per auditor review):
+        spacing = hole_span / (hole_count - 1)
+        ligament = spacing - holes_diameter
+
+    Args:
+        holes_diameter: Hole diameter in mm.
+        hole_count: Number of holes (integer ≥ 2).
+
+    Returns:
+        Ligament width in mm. Negative means overlap.
+    """
+    if hole_count < 2:
+        # Single hole — no overlap possible, return large ligament
+        return HOLE_SPAN
+    spacing = HOLE_SPAN / (hole_count - 1)
+    return spacing - holes_diameter
+
+
+def compute_web_clearance(
+    beam_face_thickness: float, holes_diameter: float
+) -> float:
+    """Compute clearance between hole edge and face sheets.
+
+    Total beam height = 2 × beam_half_height = 500 mm (fixed).
+    Web clear height = total_height - 2 × face_thickness.
+    Clearance = web_clear_height - holes_diameter.
+
+    Args:
+        beam_face_thickness: Face sheet thickness in mm.
+        holes_diameter: Hole diameter in mm.
+
+    Returns:
+        Web clearance in mm. ≤ 0 means hole doesn't fit.
+    """
+    total_height = 2.0 * BEAM_HALF_HEIGHT  # 500 mm
+    web_clear_height = total_height - 2.0 * beam_face_thickness
+    return web_clear_height - holes_diameter
+
+
+def check_feasibility(point: DesignPoint) -> FeasibilityResult:
+    """Run all geometric feasibility checks on a design point.
+
+    Checks (in order):
+        1. Hole overlap — ligament between adjacent holes ≥ MIN_LIGAMENT
+        2. Web clearance — hole fits within the web (between face sheets)
+
+    Args:
+        point: Design variable combination to check.
+
+    Returns:
+        FeasibilityResult with feasibility status and diagnostic info.
+    """
+    ligament = compute_ligament(point.holes_diameter, point.hole_count)
+    web_clearance = compute_web_clearance(
+        point.beam_face_thickness, point.holes_diameter
+    )
+
+    # Check 1: Hole overlap
+    if ligament < MIN_LIGAMENT:
+        return FeasibilityResult(
+            feasible=False,
+            reason=(
+                f"Hole overlap: ligament={ligament:.1f}mm < "
+                f"{MIN_LIGAMENT}mm minimum "
+                f"(d={point.holes_diameter}mm, n={point.hole_count})"
+            ),
+            ligament=ligament,
+            web_clearance=web_clearance,
+        )
+
+    # Check 2: Web clearance
+    if web_clearance <= 0:
+        return FeasibilityResult(
+            feasible=False,
+            reason=(
+                f"Hole exceeds web: clearance={web_clearance:.1f}mm ≤ 0 "
+                f"(face={point.beam_face_thickness}mm, "
+                f"d={point.holes_diameter}mm)"
+            ),
+            ligament=ligament,
+            web_clearance=web_clearance,
+        )
+
+    return FeasibilityResult(
+        feasible=True,
+        reason="OK",
+        ligament=ligament,
+        web_clearance=web_clearance,
+    )
+
+
+def check_feasibility_from_values(
+    beam_half_core_thickness: float,
+    beam_face_thickness: float,
+    holes_diameter: float,
+    hole_count: int,
+) -> FeasibilityResult:
+    """Convenience wrapper — check feasibility from raw DV values.
+
+    Args:
+        beam_half_core_thickness: Core half-thickness in mm (DV1).
+        beam_face_thickness: Face sheet thickness in mm (DV2).
+        holes_diameter: Hole diameter in mm (DV3).
+        hole_count: Number of holes (DV4).
+
+    Returns:
+        FeasibilityResult with feasibility status and diagnostic info.
+    """
+    point = DesignPoint(
+        beam_half_core_thickness=beam_half_core_thickness,
+        beam_face_thickness=beam_face_thickness,
+        holes_diameter=holes_diameter,
+        hole_count=hole_count,
+    )
+    return check_feasibility(point)
+
+
+# ---------------------------------------------------------------------------
+# Quick self-test
+# ---------------------------------------------------------------------------
+if __name__ == "__main__":
+    # Baseline: should be feasible
+    baseline = DesignPoint(
+        beam_half_core_thickness=25.162,
+        beam_face_thickness=21.504,
+        holes_diameter=300.0,
+        hole_count=10,
+    )
+    result = check_feasibility(baseline)
+    print(f"Baseline: {result}")
+    assert result.feasible, f"Baseline should be feasible! Got: {result}"
+
+    # Worst case: n=15, d=450 — should be infeasible (overlap)
+    worst_overlap = DesignPoint(
+        beam_half_core_thickness=25.0,
+        beam_face_thickness=20.0,
+        holes_diameter=450.0,
+        hole_count=15,
+    )
+    result = check_feasibility(worst_overlap)
+    print(f"Worst overlap: {result}")
+    assert not result.feasible, "n=15, d=450 should be infeasible"
+
+    # Web clearance fail: face=40, d=450
+    web_fail = DesignPoint(
+        beam_half_core_thickness=25.0,
+        beam_face_thickness=40.0,
+        holes_diameter=450.0,
+        hole_count=5,
+    )
+    result = check_feasibility(web_fail)
+    print(f"Web clearance fail: {result}")
+    assert not result.feasible, "face=40, d=450 should fail web clearance"
+
+    print("\nAll self-tests passed ✓")