Add Hydrotech Beam project files - CONTEXT.md and TECHNICAL_BREAKDOWN.md

Project intake and technical breakdown for beam structural optimization.
4 design variables, SOL 101, single-objective (minimize mass).

projects/hydrotech-beam/1_breakdown/TECHNICAL_BREAKDOWN.md

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+# Technical Breakdown — Hydrotech Beam Structural Optimization
+
+**Project:** Hydrotech Beam  
+**Protocol:** OP_10 (Project Intake), Step 2 — Technical Breakdown  
+**Author:** Technical Lead 🔧  
+**Date:** 2025-02-09  
+**Status:** Ready for review  
+
+---
+
+## 1. Geometry Description & Structural Behavior
+
+### 1.1 Structural Configuration
+
+The component is a **sandwich I-beam** serving as the primary load-bearing member in a test fixture assembly. Key geometric features:
+
+- **Cross-section:** Sandwich construction — a core layer flanked by face sheets on top and bottom flanges
+- **Web:** Contains a pattern of **lightening holes** (circular cutouts) to reduce mass
+- **Loading:** Static structural — likely a cantilever or simply-supported configuration with transverse loading (evidenced by "tip displacement" as a key output)
+- **Material:** Steel (AISI) — conservatively strong for this application, which is consistent with the "overbuilt" assessment
+
+### 1.2 Structural Behavior Analysis
+
+The beam behaves as a **bending-dominated structure**. Key physics:
+
+| Behavior | Governing Parameters | Notes |
+|----------|---------------------|-------|
+| **Bending stiffness (EI)** | Face thickness, core thickness | Sandwich theory: faces carry bending stress, core carries shear. Stiffness scales roughly with the square of the distance from the neutral axis |
+| **Mass** | All four variables | Core thickness and face thickness add material directly; holes remove material from the web |
+| **Stress concentrations** | Hole diameter, hole spacing | Larger holes → higher stress concentration factors at hole edges. Closely spaced holes can have interacting stress fields |
+| **Shear capacity** | Core thickness, hole count, hole diameter | Web lightening holes reduce shear area. More holes or larger holes = less shear-carrying web |
+| **Local buckling** | Face thickness, hole geometry | Thin faces or large unsupported spans between holes may introduce local instability, though at steel gauges this is less likely |
+
+### 1.3 Baseline Assessment
+
+The current design (~974 kg, ~22 mm tip displacement) is **significantly overbuilt** in mass but **under-stiff** relative to the 10 mm displacement target. This is an important observation:
+
+> ⚠️ **The baseline FAILS the displacement constraint.** Tip displacement is 22 mm vs. a 10 mm limit. This means the optimizer must simultaneously **increase stiffness (reduce displacement by >50%)** while **reducing mass**. These objectives are naturally conflicting — stiffer generally means heavier.
+
+This will drive the optimizer toward a specific region: **thicker faces** (increased bending stiffness) but **thinner core** and/or **more/larger holes** (reduced mass). The feasible region may be narrow.
+
+---
+
+## 2. Design Variable Assessment
+
+### 2.1 Individual Variable Analysis
+
+| Variable | ID | Range | Type | Sensitivity Expectation | Primary Effect |
+|----------|----|-------|------|------------------------|----------------|
+| `beam_half_core_thickness` | DV1 | 10–40 mm | Continuous | **High** on mass, **Medium** on stiffness | Increases distance between face sheets → stiffness scales ~quadratically. Also adds core mass. |
+| `beam_face_thickness` | DV2 | 10–40 mm | Continuous | **High** on both mass and stiffness | Thicker faces = more bending stiffness AND more mass. Key trade-off variable. |
+| `holes_diameter` | DV3 | 150–450 mm | Continuous | **High** on mass, **High** on stress | Larger holes remove more web material (mass ∝ d²). But stress concentrations scale with hole size. |
+| `hole_count` | DV4 | 5–15 | **Integer** | **Medium** on mass, **Medium** on stress | More holes = less web mass, but also less shear-carrying area and potential hole interaction effects |
+
+### 2.2 Interaction Effects (Expected)
+
+These variables are **not independent** — significant interactions are expected:
+
+1. **DV1 × DV2 (core × face):** Classic sandwich interaction. Optimal bending stiffness comes from balancing core depth (lever arm) vs. face material (bending resistance). Increasing core thickness makes face thickness more effective for stiffness.
+
+2. **DV3 × DV4 (hole diameter × hole count):** Strong interaction. Both control how much web material is removed. Large holes + many holes could create a web that's more hole than steel — stress will spike. There may be a **feasibility boundary** where the holes start to overlap or leave insufficient ligament width between them.
+
+3. **DV2 × DV3 (face × hole diameter):** Stress at hole edges depends on the overall stress field, which is influenced by face sheet proportioning. Thicker faces reduce nominal stress → allowing larger holes.
+
+4. **DV1 × DV3 (core × hole diameter):** Core thickness determines beam depth → determines web height → constrains maximum feasible hole diameter. If `holes_diameter` can approach the web height, we need a geometric feasibility check.
+
+### 2.3 Discrete Variable Handling — `hole_count`
+
+`hole_count` is an **integer variable** (5–15, 11 levels). Options:
+
+| Approach | Pros | Cons |
+|----------|------|------|
+| **Treat as continuous, round at end** | Simple, works with any algorithm | Rounding may violate constraints; NX may not accept non-integer |
+| **Treat as truly integer** | Correct physics per evaluation | Limits algorithm choices; some optimizers handle poorly |
+| **Relaxed continuous + periodic integer check** | Best of both worlds | More complex implementation |
+
+**Recommendation:** Treat `hole_count` as **integer throughout**. With only 11 levels and NX-in-the-loop (where the model must be rebuilt with integer hole count), there's no benefit to continuous relaxation. The algorithms recommended below (CMA-ES, TPE) both handle mixed integer/continuous natively.
+
+---
+
+## 3. Objective Formulation
+
+### 3.1 Single-Objective vs. Multi-Objective
+
+The handoff mentions three goals: minimize mass, minimize displacement, keep stress safe. Let's decompose:
+
+| Goal | Type | Rationale |
+|------|------|-----------|
+| Minimize mass | **Primary objective** | Antoine's explicit priority |
+| Tip displacement < 10 mm | **Constraint** | Hard limit, not a competing objective |
+| Von Mises stress < 130 MPa | **Constraint** | Hard limit (safety) |
+
+**Recommendation: Single-objective optimization.**
+
+$$\min_{x} \quad f(x) = \text{mass}(x)$$
+$$\text{s.t.} \quad g_1(x) = \delta_{\text{tip}}(x) \leq 10 \text{ mm}$$
+$$\quad\quad g_2(x) = \sigma_{\text{VM,max}}(x) \leq 130 \text{ MPa}$$
+
+Rationale:
+- Mass is the clear primary objective
+- Displacement and stress are hard constraints, not competing objectives to trade off
+- Single-objective is simpler, converges faster, and is appropriate for 4 design variables
+- If Antoine later wants to explore the Pareto front (mass vs. displacement), we can reformulate
+
+### 3.2 Constraint Margins
+
+Given that the baseline **already violates** the displacement constraint, we should consider:
+- Running the optimizer **without constraint penalties initially** to map the landscape
+- Using a **penalty-based** approach with gradually increasing penalty weight
+- Or using **feasibility-first** ranking (preferred for population-based methods)
+
+**Recommendation:** Use a constraint-handling approach where feasible solutions always rank above infeasible ones (Deb's feasibility rules), with infeasible solutions ranked by constraint violation magnitude.
+
+---
+
+## 4. Constraint Formulation — Extraction from NX
+
+### 4.1 Mass (Objective)
+
+- **Source:** NX expression `p173`
+- **Extraction:** Read directly from the NX expression system after model update
+- **Units:** kg
+- **Validation:** Cross-check with manual volume × density at baseline
+
+### 4.2 Tip Displacement (Constraint g₁)
+
+- **Source:** NX Nastran SOL 101 results — nodal displacement
+- **Extraction method options:**
+  1. **DRESP1 in the .sim:** Define a displacement response at the tip node(s). Extract max magnitude from the .f06 or .op2 results file
+  2. **Post-processing script:** Parse the Nastran output (.f06 or .op2) for the displacement at the tip node ID
+  3. **NX expression/sensor:** If a result sensor is defined in the sim, it can be queried as an expression
+- **Recommended:** Define a **displacement result sensor** in `Beam_sim1.sim` at the beam tip. This gives us a clean NX expression we can extract alongside `p173`
+- **Component:** We need to clarify whether the constraint is on **total magnitude** (RSS of X, Y, Z) or a **single component** (likely vertical/Z displacement). Assume magnitude for now.
+
+### 4.3 Von Mises Stress (Constraint g₂)
+
+- **Source:** NX Nastran SOL 101 elemental/nodal stress results
+- **Extraction method options:**
+  1. **DRESP1:** Maximum von Mises stress across the model or a specific group
+  2. **Result sensor:** Max stress sensor in the sim
+  3. **Post-processing:** Parse peak stress from .f06
+- **Recommended:** Define a **stress result sensor** for max von Mises. Critical: identify the **stress reporting location** — element centroid vs. corner nodes can differ by 10–20%
+- **Concern:** Stress at hole edges will be mesh-sensitive. Need to ensure mesh convergence at holes (see Section 5)
+
+### 4.4 Extractor Requirements
+
+The Atomizer framework will need extractors for:
+1. `mass` ← NX expression `p173`
+2. `tip_displacement` ← displacement sensor or Nastran output parse
+3. `max_von_mises` ← stress sensor or Nastran output parse
+
+> ⚠️ **Action needed:** Confirm whether result sensors already exist in `Beam_sim1.sim`, or whether we need to create them. This determines extractor complexity.
+
+---
+
+## 5. Solver Requirements
+
+### 5.1 Solution Type
+
+- **SOL 101 (Linear Static)** — appropriate for this problem
+- Steel under moderate loading → linear elastic behavior expected
+- Small displacement assumption: 22 mm tip displacement on a beam that's likely 2+ meters long → probably OK, but should verify L/δ ratio
+- If L/δ < 50, consider SOL 106 (geometric nonlinearity) — **unlikely to be needed**
+
+### 5.2 Mesh Considerations
+
+| Concern | Requirement | Priority |
+|---------|-------------|----------|
+| **Hole edge refinement** | Stress accuracy at lightening holes requires adequate mesh density. At minimum 4–6 elements around each hole quarter-circumference | **Critical** |
+| **Mesh morphing vs. remeshing** | When `holes_diameter` or `hole_count` changes, does the mesh adapt? Parametric NX models typically **remesh** on update — need to confirm | **High** |
+| **Mesh convergence** | Must verify that the baseline mesh gives converged stress results. If not, results will be noisy and optimization will struggle | **Critical** |
+| **Element type** | Confirm element type: CQUAD4/CQUAD8 for shell? CTETRA/CHEXA for solid? Shell elements for thin faces are more efficient | **Medium** |
+| **Mesh size consistency** | If mesh density varies with design variable changes, the noise in the objective/constraints could mislead the optimizer | **High** |
+
+### 5.3 Solver Runtime
+
+- Need to benchmark: **how long does one SOL 101 run take?** This directly determines feasible trial budget
+- Estimated: for a single beam with ~10K–100K DOF → probably **seconds to low minutes** per evaluation
+- If < 2 minutes per run → budget of 100–200 trials is very feasible
+
+---
+
+## 6. Algorithm Recommendation
+
+### 6.1 Problem Characterization
+
+| Dimension | Value |
+|-----------|-------|
+| Design variables | 4 (3 continuous + 1 integer) |
+| Objectives | 1 (mass) |
+| Constraints | 2 (displacement, stress) |
+| Evaluation cost | Medium (NX model update + SOL 101 solve) |
+| Landscape | Expected smooth with possible local features near constraint boundaries |
+| Variable interactions | Significant (sandwich theory, hole interaction) |
+
+### 6.2 Algorithm Comparison
+
+| Algorithm | Handles Integer? | Handles Constraints? | Trial Efficiency | Exploration | Notes |
+|-----------|-----------------|---------------------|-----------------|-------------|-------|
+| **CMA-ES** | Yes (with rounding) | Via penalty/repair | Good for 4D | Excellent | Strong for low-dimensional continuous; integer handling is approximate |
+| **TPE (Bayesian)** | Yes (natively) | Via constraint observations | Excellent | Good | Optuna's default; handles mixed types well; sample-efficient |
+| **NSGA-II** | Yes | Yes (Pareto-based) | Moderate | Excellent | Overkill for single-objective; better for multi-obj |
+| **Nelder-Mead** | No | Via penalty | Moderate | Poor | Too simple for mixed-integer |
+| **SOL 200 (Nastran)** | Limited | Yes (native) | Excellent (gradient) | Poor | Nastran-native; no integer support; gradient-based so fast convergence but may miss global optimum |
+| **Latin Hypercube + Surrogate** | Yes | Yes | High (via surrogate) | Excellent | Build surrogate from DoE, optimize on surrogate. Very efficient for expensive sims |
+
+### 6.3 Recommended Approach: **Two-Phase Strategy**
+
+#### Phase 1: Design of Experiments (DoE) — Landscape Mapping
+- **Method:** Latin Hypercube Sampling (LHS)
+- **Budget:** 40–50 evaluations
+- **Purpose:**
+  - Map the design space
+  - Identify feasible region
+  - Understand variable sensitivities and interactions
+  - Build intuition before optimization
+  - Catch any model failures or numerical issues early
+- **Output:** Sensitivity plots, interaction plots, feasible region visualization
+
+#### Phase 2: Directed Optimization — TPE (Tree-structured Parzen Estimator)
+- **Method:** TPE via Optuna
+- **Budget:** 60–100 evaluations
+- **Purpose:**
+  - Exploit the landscape knowledge from Phase 1
+  - Converge to the optimum
+- **Why TPE over CMA-ES:**
+  - Native mixed-integer support (no rounding hacks for `hole_count`)
+  - Built-in constraint handling via Optuna's constraint interface
+  - Sample-efficient — important if NX solve time is non-trivial
+  - Handles non-smooth constraint boundaries well (stress around holes can have sharp gradients)
+  - Well-supported in Python/Optuna ecosystem
+
+#### Total Budget: ~100–150 NX evaluations
+
+At 1–2 minutes per evaluation → **2–5 hours total compute time**. Very manageable.
+
+### 6.4 Alternative: SOL 200 for Continuous Subproblem
+
+If we fix `hole_count` at a few integer values (e.g., 7, 10, 13), we could run **Nastran SOL 200** for the remaining 3 continuous variables at each fixed hole count. SOL 200 uses gradient-based optimization with analytical sensitivities — extremely efficient. Then pick the best across the integer levels.
+
+**Pros:** Fastest convergence for continuous variables, leverages Nastran's native sensitivity analysis  
+**Cons:** Requires DESVAR/DRESP setup in the .sim, more NX expertise, less framework-portable
+
+**Verdict:** Keep as a **backup option**. TPE is more aligned with the Atomizer framework approach and handles the full mixed-integer problem in one pass.
+
+---
+
+## 7. Gap Analysis
+
+### 7.1 Must-Clarify Before Proceeding
+
+| # | Item | Why It Matters | Risk if Unresolved |
+|---|------|---------------|-------------------|
+| G1 | **Beam length and support conditions** | Need to understand L/δ ratio; affects whether linear analysis is sufficient; affects sensitivity expectations | Could invalidate SOL 101 assumption |
+| G2 | **Loading definition** | What loads are applied? Point load at tip? Distributed? Self-weight? This affects stress distribution and which variables matter most | Incorrect optimization direction |
+| G3 | **Displacement measurement location** | "Tip displacement" — which node exactly? Max of a set? Single point? Which DOF component? | Wrong constraint extraction |
+| G4 | **Stress constraint location** | Max VM stress where? Entire model? Exclude supports/load application points? Stress at hole edges specifically? | Over-constraining or missing real failures |
+| G5 | **Geometric feasibility of hole patterns** | When `hole_count = 15` and `holes_diameter = 450 mm`, do holes overlap? What's the beam web length? | Infeasible geometries will crash NX |
+| G6 | **Result sensors in the sim** | Do `Beam_sim1.sim` already have displacement/stress sensors defined? | Determines extractor development effort |
+| G7 | **NX model parametric update method** | How are design variables linked to NX expressions? Does the model reliably rebuild across the full range? | Model rebuild failures during optimization |
+| G8 | **Mesh type and density** | Shell or solid elements? Current mesh size? Has convergence been checked? | Noisy results → poor optimization |
+| G9 | **Stress allowable basis** | 130 MPa — is this yield with a safety factor? What factor? Is it a project spec? | Constraint may be wrong |
+
+### 7.2 Nice-to-Know
+
+| # | Item | Value |
+|---|------|-------|
+| N1 | Any previous optimization attempts on this beam? | Avoids repeating failed approaches |
+| N2 | Are there manufacturing constraints (min face thickness, standard hole sizes)? | May restrict feasible designs |
+| N3 | Is fatigue a concern? | Static optimization alone may not be sufficient |
+| N4 | Any other load cases (dynamic, thermal, handling)? | Current scope is single static case |
+| N5 | Target mass? Antoine says "lighter" — is there a specific mass goal? | Helps gauge success criteria |
+
+---
+
+## 8. Risk Assessment
+
+### 8.1 Risk Register
+
+| # | Risk | Likelihood | Impact | Mitigation |
+|---|------|-----------|--------|------------|
+| R1 | **Narrow feasible region** — displacement constraint is already violated at baseline. The feasible region (displacement < 10 mm AND low mass) may be very small or empty | **High** | **Critical** | Run DoE first to map feasibility. If no feasible point found, discuss relaxing constraints with Antoine |
+| R2 | **NX model rebuild failures** — parametric models can fail at extreme variable combinations (geometry boolean failures, mesh errors) | **Medium** | **High** | Test all 4 corners of the design space manually before optimization. Implement robust error handling |
+| R3 | **Mesh-dependent stress results** — stress at hole edges is mesh-sensitive. If the mesh changes character across the design space, stress results may be inconsistent | **Medium** | **High** | Conduct mesh convergence study at baseline. Verify mesh quality at 2–3 points in the design space |
+| R4 | **Conflicting objectives** — reducing mass while halving displacement requires finding a very specific structural configuration | **High** | **Medium** | The sandwich effect is our ally: increasing core depth increases stiffness faster than mass. But the feasible region may demand thick faces |
+| R5 | **Hole overlap at extreme parameters** — high hole count + large diameter could create infeasible geometry | **Medium** | **Medium** | Add a geometric feasibility pre-check before NX evaluation. Calculate minimum ligament width |
+| R6 | **Linear analysis limitation** — if optimal design has very thin members, local buckling or geometric nonlinearity could invalidate results | **Low** | **Medium** | Post-optimization validation: run SOL 105 (buckling) and/or SOL 106 on final design |
+| R7 | **Single load case optimization** — optimizing for one load case may create a design that fails under other real-world conditions | **Medium** | **High** | Flag to Antoine: are there other load cases? Plan verification runs post-optimization |
+
+### 8.2 Overall Risk Rating: **MEDIUM-HIGH**
+
+The primary risk driver is **R1 — the feasible region may be very constrained** (or empty). The baseline design already violates the displacement constraint. The optimization isn't just about making it lighter — it must first make it stiffer, then lighter within the stiffness constraint. This is achievable with sandwich theory (the core thickness lever arm is powerful), but we need the DoE phase to confirm.
+
+---
+
+## 9. Recommended Next Steps
+
+1. **Clarify gaps G1–G9** with Antoine (via Manager)
+2. **Baseline model validation:**
+   - Open NX model and document geometry, mesh, BCs, loading
+   - Run baseline and verify reported mass/displacement/stress values
+   - Conduct mesh convergence check
+3. **Test parametric rebuild** at design space corners
+4. **Set up extractors** for mass, displacement, stress
+5. **Execute Phase 1 DoE** (40–50 LHS samples)
+6. **Analyze DoE results** — sensitivity, feasibility, interactions
+7. **Execute Phase 2 TPE** optimization (60–100 trials)
+8. **Validate optimum** — confirm NX results, check buckling, review physics
+
+---
+
+## 10. Summary
+
+| Aspect | Recommendation |
+|--------|---------------|
+| **Formulation** | Single-objective: minimize mass, constrain displacement (≤10mm) and stress (≤130 MPa) |
+| **Algorithm** | Two-phase: LHS DoE (40–50 trials) → TPE optimization (60–100 trials) |
+| **Total budget** | ~100–150 NX evaluations |
+| **Integer handling** | `hole_count` treated as true integer (TPE native support) |
+| **Key risk** | Baseline violates displacement constraint — feasible region may be tight |
+| **Key gap** | Need to confirm loading, BCs, and geometric feasibility limits |
+| **Confidence** | **Medium** — solid approach, but dependent on gap resolution |
+
+---
+
+*Technical Lead 🔧 — The physics is the boss.*

projects/hydrotech-beam/CONTEXT.md

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+# CONTEXT.md — Hydrotech Beam Structural Optimization
+
+## Client
+Hydrotech (internal test fixture)
+
+## Objective
+Minimize beam mass while reducing tip displacement and keeping stress within limits. Multi-objective: lighter, stiffer, safe.
+
+## Key Parameters
+| Parameter | Current | Range | Units | Notes |
+|-----------|---------|-------|-------|-------|
+| beam_half_core_thickness | 20 | 10–40 | mm | Core half-thickness |
+| beam_face_thickness | 20 | 10–40 | mm | Face sheet thickness |
+| holes_diameter | 300 | 150–450 | mm | Lightening hole diameter |
+| hole_count | 10 | 5–15 | integer | Number of lightening holes |
+
+## Constraints
+- Max tip displacement: < 10 mm
+- Max von Mises stress: < ~130 MPa (steel, conservative)
+- Mass tracked via NX expression `p173`
+
+## Objectives
+- Minimize mass (currently ~974 kg — way too heavy)
+- Minimize tip displacement (currently ~22 mm, target < 10 mm)
+- Keep stress reasonable (steel, margin exists)
+
+## Baseline Performance
+- Mass: ~974 kg
+- Tip displacement: ~22 mm
+- Material: Steel (AISI)
+
+## Model
+- NX Part: `Beam.prt`
+- FEM: `Beam_fem1.fem`
+- Idealized part: `Beam_fem1_i.prt`
+- Simulation: `Beam_sim1.sim`
+- Solver: NX Nastran (static structural)
+- Analysis: Static structural
+
+## Decisions
+- 2026-02-08: Project received from Antoine
+
+## Status
+Phase: Intake
+Channel: #project-hydrotech-beam