FEM@ti
Magyarul
Elastic–plastic Timoshenko-beam finite element analysis — a modern,
TypeScript-based, validated FEA program.
Try it live → — no install needed, runs entirely in the browser.
⚠️ Not certified design software. FEM@ti is a research and educational finite element tool.
Its numerical core is validated against closed-form solutions (see
docs/VALIDATION-SCOPE.md for exactly what is and is not covered),
but all results must be verified independently, under professional engineering responsibility,
before being used for any structural design decision.
Note on language: the source comments and the deeper documentation
(docs/, ADRs) are in Hungarian — this is a personal project built around
a Hungarian engineering thesis. This README exists so an English-speaking
visitor can understand what the project does and judge its engineering/
software quality without reading Hungarian. The application's own user
interface has a full HU/EN switch (header, top right) and opens in
English by default — the physics notation (M, T, w, φ, E, G, I, A) was
always standard and language-independent regardless.
What is this?
In 1996, a thesis at the Budapest University of Technology (BME) produced an
elastic–plastic Timoshenko-beam finite element program: 3-node quadratic
beam elements, selective reduced integration (against shear locking), a
frontal equation solver, and a layered (fiber) cross-section model to track
plastic deformation.
FEM@ti reimplements the same structural-mechanics model thirty years later,
as a modern, interactive, browser-based application — not "inspired by" the
thesis, but line-by-line traceable to it: every implemented formula is
matched to the thesis's exact page and equation number (see
docs/THEORY.md), and every mechanical claim is proven by
a validation test against closed-form or hand-calculated reference values
(see docs/VALIDATION.md). For a direct answer to
"how do you know the underlying mechanics is correct, and what are you
not claiming," see docs/VALIDATION-SCOPE.md.
Wherever current software-engineering practice diverges from the 1996
solution (e.g. skyline storage instead of the frontal solver on the
production path), that divergence is recorded in a dedicated architecture
decision record (ADR) — including the ORIGINAL frontal algorithm itself,
which remains available, animated, in the app's "Historical mode" view for
teaching purposes (see ADR-0002).
Why it's worth a look
- Interactive model canvas — click/drag-editable beam model (supports,
point/distributed loads), with live recomputation on every change.
- Linear AND nonlinear (elastic–plastic) analysis — Newton–Raphson
solver with adaptive load stepping, REFORB stress return-mapping, a
load-step timeline, and plastic-zone visualization.
- Full, auditable derivation for every step — per-Gauss-point shape
function / Jacobian / B-matrix / stiffness-matrix values, layered plastic
return-mapping, with Word (.docx, real OOXML math objects) and printable
PDF export.
- Calculation report and a "Historical mode" (an animated replay of
the original 1996 frontal algorithm, side by side with today's skyline
solver).
- ~700 automated tests, including a 10,000-element fuzz test
(
fast-check) proving the solver never throws an unhandled exception and
always returns an equilibrated result on random structures.
Running it
Prerequisite: Node.js ≥ 20, pnpm 10 (the repo's packageManager
field pins the exact version — after corepack enable the correct pnpm is
picked up automatically).
pnpm install
pnpm --filter @femati/ui dev
This starts the Vite dev server — open the printed
http://localhost:5173 URL in a browser.
Verification (typecheck + lint + test, across all packages)
pnpm check
Production build
pnpm build
Monorepo layout
pnpm workspace, 4 packages:
| Package | Contents |
|---|
packages/fem-core | The actual FEM core: model, elements, solvers (skyline-LDLᵀ and the historical frontal one), material models, validation, post-processing — no DOM dependency, usable standalone. |
packages/fem-db | Material and cross-section catalog, with source attribution (every record requires a source/verified field). |
packages/fem-validation | The validation cases that GENERATE docs/VALIDATION.md (against closed-form/hand-calculated references). |
packages/ui | React + Vite client-side UI — computation runs in the browser, no backend. |
See docs/architecture.html for an interactive
diagram of how these four packages actually depend on each other (open it
in a browser) — including the distinction between what runs live in the
browser and what only runs in dev/CI (fem-validation, and fem-db's own
test suite, which checks its catalog data against fem-core's computed
properties).
The fem-db catalog browser (docs/QUICKSTART.md walks through it) — every entry ties its computed properties back to the formula that produced them.
Documentation
The app's "Elméletek" (Theories) menu exposes the same content directly in
the application, typeset with KaTeX.
Privacy
Your model never leaves your browser. All computation is client-side — there is no
backend, no upload, no account, and no synchronization. Fonts are self-hosted, so the
page contacts no third-party CDN.
The hosted demo at femati.vercel.app uses Vercel Web
Analytics to count visits: no cookies, no localStorage, no cross-site tracking, no
personal identification — page, referrer, country and device type only. It sees
nothing about your model, inputs or results. If you build and run the project yourself,
it makes no outbound requests at all. See SECURITY.md for details.
License
MIT
Built on a full read-through of the original Diplomaterv (BME).pdf
(73 pages) — every mechanical formula comes from a verified source, none
was invented.
