FEA (finite element analysis)

mcp-fea

Real finite element analysis from a conversation. An AI assistant sends a STEP file and a plain-English question ("does this arm survive a 6 g maneuver with a 400 g motor?"); this MCP server maps the words onto geometry, rejects bad setups deterministically before any compute is spent, meshes and solves with CalculiX on Modal as an async MCP task, and returns a verdict backed by numbers — peak von Mises stress, factor of safety, deflection, natural frequencies — plus rendered stress plots and an interactive 3D viewer. Every study ends with a non-skippable reaction-balance check; every benchmark on the validation page is regenerated by CI on every commit.

Measured on the live deployment (2026-07-31): cold start 3.8 s · cantilever study submit→completed 9.3 s warm / 12.9 s with a cold solver container · ~$0.002 per study at Modal's posted rates.

Benchmark	Reference	Computed	Error
Cantilever tip deflection (PL³/3EI)	0.58055 mm	0.58046 mm	0.02%
NAFEMS LE10 σ_yy @ D	−5.38 MPa	−5.456 MPa	1.41%
Plate-with-hole peak (Heywood Kt)	62.8 MPa	61.92 MPa	1.40%
Cantilever f₁ (Euler–Bernoulli)	816.0 Hz	815.4 Hz	0.08%

Full table, mesh stats, and an explicit limitations section: docs/validation.md — regenerated by CI, never hand-edited.

Protocol: MCP 2026-07-28 (stateless core) with the io.modelcontextprotocol/tasks extension implemented per SEP-2663 (the official Python SDK v2 shipped without it — this repo also contains the client-side extension that teaches the official SDK to consume task-augmented servers) and an MCP Apps (SEP-1865) 3D viewer. See docs/decisions.md for every engineering call and why.

Deploy (3 commands)

uv sync
uv run modal secret create mcp-fea-token MCP_FEA_TOKEN=$(openssl rand -hex 24)
uv run modal deploy -m src.server.modal_app

Modal prints the endpoint URL (https://<workspace>--mcp-fea-mcp-endpoint.modal.run). Connect any 2026-07-28 MCP client with Authorization: Bearer <your token>. First-time Modal users: uv run modal token new once. Then verify the live deployment end to end:

MCP_FEA_LIVE_URL=https://... MCP_FEA_TOKEN=... make verify-live

Tools

Tool	Sync/async	What it does
inspect_geometry	sync	STEP → face table (face_id, type, centroid, normal/axis, area, bbox) + part bbox/volume. Call first: it's how English maps to face ids.
list_materials	sync	Built-in library: Al 6061-T6, Al 7075-T6, Steel 4140, Stainless 304, Ti-6Al-4V, ABS, PLA, Nylon 12, PC (E, ν, yield, density).
submit_fea_study	task	Linear static: validate → mesh (C3D10, curvature-adaptive, local thin-wall refine) → CalculiX → verdict/stress/FoS + 3 stress PNGs.
submit_modal_study	task	Natural frequencies + mode shapes (*FREQUENCY), first N modes (default 6), one exaggerated-deformation PNG per mode. Requires constraints and density.
get_report	sync	Full payload for a completed task; include_mesh_data: true adds the surface-mesh payload the 3D viewer app fetches.

Task lifecycle: working (statusMessage walks validating → meshing → solving → postprocessing) → completed | failed | cancelled; tasks/cancel kills the running container. Tasks are retained 24 h.

Units policy

One conversion boundary, at ingest. Internally everything is consistent mm–N–MPa(–tonne): lengths mm, forces N, stress/moduli MPa, density tonne/mm³ (kg/m³ × 1e-12 — done once, in Material.density_tonne_mm3), which makes modal frequencies come out directly in Hz. STEP coordinates are interpreted in the declared units (mm|m|in); gmsh's own unit conversion is disabled so the declared unit is authoritative — and sanity-checked (a 100 mm part declared "m" gets flagged).

Validation codes

Every rejection returns {code, message, suggested_fix}.

Code	Meaning	Stage
GEOMETRY_REF_INVALID	STEP missing/unreadable/over 25 MB, bad units field	parse
GEOMETRY_KERNEL_CRASH / GEOMETRY_TIMEOUT	CAD kernel crashed / hung on the file (isolated subprocess; endpoint unaffected)	inspect
MATERIAL_UNKNOWN / MATERIAL_UNPHYSICAL	Not in library / E ∉ [0.01, 1500] GPa, ν ∉ (0, 0.5), yield ≤ 0, density ∉ [10, 25000] kg/m³, missing density for modal	parse
CONSTRAINT_INVALID / CONSTRAINT_CONFLICT	Bad type; node pinned in two local frames	parse/deck
LOAD_INVALID / LOAD_MISSING / MODAL_INVALID	Bad type/units/direction; zero loads; bad n_modes	parse
GEOM_NO_SOLID / GEOM_MULTIPLE_SOLIDS	Not a single solid body (assemblies = v2)	pre-mesh
FACE_ID_INVALID	Face id not on this part	pre-mesh
RIGID_BODY_MOTION	Constraints leave free motion (named, e.g. "rotation about the hole axis") — SVD rank check	pre-mesh
LOAD_ON_FIXED_FACE	Load applied to a fully fixed face	pre-mesh
UNITS_SUSPECT (warning)	Part > 5 m or < 0.5 mm — declared units probably wrong	pre-mesh
LOAD_MAGNITUDE_EXTREME / _NEGLIGIBLE (warnings)	σ ≈ F/A > 10× yield or < 1e-6× yield	pre-mesh
MESH_ELEMENT_CAP	> 400k elements even after coarsening / local refine	mesh
MESH_QUALITY_JACOBIAN / MESH_QUALITY_ASPECT / MESH_THIN_WALLS	Quality gates; thin walls get one local auto-refine first	mesh
MESH_TIMEOUT	Meshing exceeded its wall budget (near-tangent slivers, helical threads) — the worker is killed from outside	mesh
SOLVER_SINGULAR / SOLVER_MESH_DEGENERATE / SOLVER_TIMEOUT / SOLVER_FAILED	Mapped ccx failures (>150k elements auto-switch to the iterative solver)	solve
EQUILIBRIUM_FAIL (warning, untrusted result)	ΣRF vs free-node applied loads off by > 0.5%	post
LOAD_INTO_SUPPORT (warning)	> 5% of the load lands on constrained nodes (loaded face touches a fixed face) and is carried directly by the support	post
BEYOND_YIELD / LARGE_DEFLECTION (warnings)	FoS < 1 (post-yield numbers flagged non-physical) / u > 5% of min dimension	post

Abuse limits (all env-tunable)

25 MB STEP cap · 40 MB request cap (413) · per-token rate limit (MCP_FEA_RATE_LIMIT/_WINDOW_S, 429) · concurrent-solve cap (MCP_FEA_MAX_CONCURRENT) · daily budget (MCP_FEA_MAX_SPAWNS_PER_DAY) · kill switch (MCP_FEA_DISABLE_SPAWN=1). CAD parsing never runs in the endpoint process (see SECURITY.md).

Local development

uv sync
curl -Ls https://micro.mamba.pm/api/micromamba/osx-arm64/latest | tar -xj bin/micromamba
./bin/micromamba create -y -p .tools/ccx-env -c conda-forge calculix=2.23
make test        # fast suite (protocol, benchmarks, validation, hardening)
make torture     # 21 real-world STEP files through the endpoint
make validation-page
uv run uvicorn --factory src.server.app:create_local_app --port 8000  # local server

Repo map

src/pipeline/ geometry, meshing, deck, solver, validation, post, render · src/materials/ library · src/server/ protocol, tools, tasks, limits, worker host, Modal app, Apps UI · src/client/ SDK tasks extension · tests/ (incl. torture/) · demo/ · docs/ decisions, validation, upstream notes. License: Apache-2.0.