Atomizer/projects/isogrid-dev-plate/BREAKDOWN.md

Technical Breakdown — Adaptive Isogrid Plate Lightweighting

Project: Isogrid Dev Plate Author: Technical Lead 🔧 Date: 2026-02-18 Status: Architecture complete — Campaign 01 ready to run

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1. Problem Formulation

1.1 Structural Configuration

Flat plate with bolt holes, optimized by replacing solid material with an adaptive triangular isogrid.

• 2 sandbox regions (sandbox_1, sandbox_2) — where ribs are generated and changed each iteration
• Bolt holes: excluded from pocket generation (keepout zone around each hole)
• Plate material: AL7075-T6 (confirmed 2026-02-18 — see material discrepancy note in §4.2)
• 3D solid FEA already run (CHEXA/CTETRA, SOL 101)

1.2 Objective Function

Single-objective: minimize total plate mass.

minimize:    mass(params)
subject to:  max_von_mises ≤ σ_allow = 100.6 MPa

No displacement constraint — confirmed by Antoine 2026-02-18.

The penalty approach:

penalty = 0.0
if max_stress > sigma_allow:
    penalty += 1e4 * ((max_stress / sigma_allow) - 1.0) ** 2
return mass_kg + penalty

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2. Design Variable Classification

2.1 Optimized Variables (8) — Atomizer design space

These directly control rib pattern shape and density. Every trial samples all 8.

Variable	Range	Description
eta_0	[0.0, 0.4]	Baseline density offset — global rib density floor
alpha	[0.3, 2.0]	Hole influence scale — how much ribs cluster around holes
beta	[0.0, 1.0]	Edge influence scale — how much ribs reinforce the perimeter
gamma_stress	[0.0, 1.5]	Stress feedback gain — how much FEA stress adds density
R_0	[10, 100] mm	Base influence radius — how far hole influence spreads
R_edge	[5, 40] mm	Edge influence radius — depth of perimeter reinforcement band
s_min	[15, 35] mm	Minimum triangle edge length → densest zone spacing (manufacturing floor: 15 mm)
s_max	[40, 60] mm	Maximum triangle edge length → sparsest zone spacing (lower bound 40 guarantees s_min < s_max)

Total: 8 continuous variables. Manageable for Optuna TPE; expect useful signal in 50–100 trials, convergence in 200–500.

2.2 Manufacturing Constraints (Fixed) — NOT optimized

These are set from machining requirements and are fixed for the entire campaign. They can be adjusted between campaigns if the process changes.

Parameter	Fixed Value	Why Fixed	Manufacturing Basis
t_min	2.5 mm	Minimum rib thickness: thinner ribs are not machinable and would break	CNC milling minimum land width
t_0	3.5 mm	Nominal rib thickness: baseline starting width before density scaling	Design intent
w_frame	5.0 mm	Perimeter frame width: solid band around the sandbox boundary	Edge seal, clamping, aesthetics
r_f	1.5 mm	Pocket fillet radius: corner radius on each pocket. Sole pocket size filter.	= tool radius. Smaller → need smaller endmill
d_keep	1.2×	Hole keepout multiplier: minimum clear distance = 1.2 × hole diameter	Prevents thin walls around bolt holes
min_triangle_area	25.0 mm²	Minimum pocketable triangle area	Below this: too small to machine → skip as solid

To change manufacturing constraints for a campaign, edit MANUFACTURING_CONSTRAINTS in optimization_engine/isogrid/study.py and document the change here.

2.3 Math/Model Constants (Fixed) — NOT optimized

These govern the mathematical form of the density field. Fixed at well-behaved defaults. Changing them would fundamentally change the shape of the density function.

Parameter	Fixed Value	Description
p	2.0	Gaussian decay exponent (p=2 → smooth Gaussian, p=1 → exponential, p=4 → box-like)
kappa	1.0	Weight-to-radius coupling: heavier holes get proportionally larger influence radius
gamma	1.0	Density-to-thickness coupling: t(x) = t₀ × (1 + γ·η)

Note: gamma here is the rib-thickness coupling, distinct from gamma_stress (stress feedback gain).

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3. Density Field Formulation

The full adaptive formula with stress feedback:

η(x,y) = clamp(0, 1, η₀ + α·I(x) + β·E(x) + γ_stress·S_stress(x))

Where:

• I(x) = Σᵢ wᵢ · exp(-(dᵢ/Rᵢ)^p) — hole influence (sum over all bolt holes)
• E(x) = exp(-(d_edge/R_edge)^p) — edge reinforcement
• S_stress(x) — normalized FEA stress field from previous trial, ∈ [0..1]
• Rᵢ = R₀ · (1 + κ · wᵢ) — per-hole radius scales with hole weight

Local spacing: s(x) = s_max - (s_max - s_min) · η(x) Local rib thickness: t(x) = clip(t₀ · (1 + γ · η(x)), t_min, t_max)

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4. FEA Pipeline Status

4.1 What Is Done

Step	Status	Notes
NX geometry extraction (extract_sandbox.py)	✅ Done	geometry_sandbox_1.json, geometry_sandbox_2.json
Python Brain (density → profile)	✅ Done	Gmsh Frontal-Delaunay, Shapely pockets
NX rib import (import_profile.py)	✅ Done	Update-in-place, preserves extrude reference
3D solid FEA (manual baseline)	✅ Done	OP2 results available
Stress field extraction (OP2 → 2D)	✅ Done	optimization_engine/extractors/extract_stress_field_2d.py
Stress feedback field	✅ Done	optimization_engine/isogrid/stress_feedback.py
Atomizer study wiring	✅ Done	studies/01_v1_tpe/run_optimization.py
Campaign 01 execution	🔴 Not started	Run run_optimization.py

4.2 FEA Configuration

• Solver: NX Nastran, SOL 101 (linear static)
• Elements: 3D solid (CHEXA, CTETRA, CPENTA)
• Stress units: NX kg-mm-s outputs kPa → extractor divides by 1000 → MPa
• Material (optimization): AL7075-T6 — σ_yield = 503 MPa, ρ = 2810 kg/m³, SF = 5 → σ_allow = 100.6 MPa
• Sandbox regions: 2 (sandbox_1 is larger, sandbox_2 is smaller patch)

⚠️ Material discrepancy (Gap G-01): The NX FEM model (MAT1 card in the DAT file) uses E = 68.98 GPa and ρ = 2.711×10⁻⁶ kg/mm³, which correspond to AL6061-T6 properties. Optimization allowables and mass targets are based on AL7075-T6 as confirmed by Antoine. This discrepancy means FEA stiffness/mass are slightly underestimated. Tracked as G-01 in CONTEXT.md — update MAT1 card before next FEA campaign.

4.3 Key FEA Files

NX model (reference copies — do NOT modify):

projects/isogrid-dev-plate/models/
├── ACS_Stack_Main_Plate_Iso_Project.prt              ← Geometry part
├── ACS_Stack_Main_Plate_Iso_project_fem2_i.prt       ← Idealized part (CRITICAL for mesh update)
├── ACS_Stack_Main_Plate_Iso_project_fem2.fem         ← FEM (3D solid, CHEXA/CTETRA)
├── ACS_Stack_Main_Plate_Iso_project_sim2.sim         ← SOL 101 simulation
└── acs_stack_main_plate_iso_project_sim2-solution_1.op2  ← Baseline FEA results

Working copies (used by optimizer):

studies/01_v1_tpe/1_setup/model/
├── ACS_Stack_Main_Plate_Iso_Project.prt
├── ACS_Stack_Main_Plate_Iso_project_fem2_i.prt
├── ACS_Stack_Main_Plate_Iso_project_fem2.fem
├── ACS_Stack_Main_Plate_Iso_project_sim2.sim
└── adaptive_isogrid_data/
    ├── geometry_sandbox_1.json   ← Sandbox boundary + holes
    └── geometry_sandbox_2.json

Python Brain (canonical location):

optimization_engine/isogrid/
├── density_field.py               ← η(x) field computation
├── triangulation.py               ← Gmsh Frontal-Delaunay mesh
├── pocket_profiles.py             ← Inset + fillet pockets
├── stress_feedback.py             ← StressFeedbackField (RBF interpolator)
└── study.py                       ← PARAM_SPACE, MANUFACTURING_CONSTRAINTS, MATERIAL

optimization_engine/extractors/
└── extract_stress_field_2d.py     ← OP2+BDF → 2D stress field

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5. Rib Pattern Variants Tested

Three density field configurations were tested for visual review in NX:

Variant	α	β	Pockets (S1+S2)	Mass Est.	Character
Balanced	1.0	0.3	86 + 33 = 119	~2,790g	Good general pattern
Edge-focused	0.3	1.5	167 + 10 = 177	~2,328g	Dense perimeter, sparse center
Hole-focused	1.8	0.15	62 + 37 = 99	~3,025g	Dense around holes, thin edges

All three were imported to NX using the update-in-place workflow (sketch preserved, extrude reference maintained).

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6. Algorithm Recommendation

Optuna TPE (Tree-structured Parzen Estimator) — standard Atomizer configuration.

Property	Value
Design variables	8 continuous
Objective	1 (minimize mass)
Constraint	1 (stress — penalty-based; no displacement constraint)
Trials budget	200 (Campaign 01)
Estimated iteration time	~90–120 sec (NX mesh + Nastran + extract)
Total runtime estimate	~8–10 hours for 200 trials

In V1, gamma_stress is sampled by TPE but has no effect (no S_prev stress field available). In V2 (sequential seeding), S_prev is loaded from the globally best previous trial; gamma_stress then actively reshapes the density field toward high-stress zones. No extra FEA per trial.

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7. Next Steps

Priority	Action	Status
✅ DONE	studies/01_v1_tpe/run_optimization.py created	—
✅ DONE	Material confirmed: AL7075-T6, σ_allow = 100.6 MPa (SF=5)	—
✅ DONE	Model files copied to studies/01_v1_tpe/1_setup/model/	—
✅ DONE	Geometry JSONs in 1_setup/model/adaptive_isogrid_data/	—
🔴 HIGH	Run Campaign 01: python studies/01_v1_tpe/run_optimization.py	Pending
🟡 MED	Update MAT1 card in NX model to AL7075-T6 properties (Gap G-01)	Pending
🟡 MED	Extract baseline solid plate mass (Gap G-02)	Pending
🟢 LOW	Benchmark single iteration time for runtime planning	Pending

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Technical Lead 🔧 — 8 parameters, physics-driven, stress-only constraint, ready to run.