Using Awatif Buckling

1Scope

Awatif Buckling solves geometrically nonlinear 3D frames and triangular shells, including P–Δ effects and post-buckling deformation. Supply a mesh, supports, nodal loads and elastic properties; receive deformed positions and frame forces. See the theory and frame benchmarks or try the interactive demo.

The demo shows results precomputed with the solver; the solver itself is not published. For integration in your own application, request a licensed build.

2First solve

Use the solver with a JavaScript module bundler that supports TypeScript and WebAssembly assets, such as the repository’s Vite setup. The import below assumes your app entry sits beside getNlPositionsAndForces.ts; adjust it to your integration. Keep the supplied WebAssembly assets with the wrapper. Await initialization once, then call the synchronous solve function.

import {
  initNlPositionsAndForces,
  getNlPositionsAndForces,
} from "./getNlPositionsAndForces";

await initNlPositionsAndForces();

// A 3 m cantilever, divided into five frame elements. Units: kN, m.
const nodes = Array.from({ length: 6 }, (_, i) => [0, 0, i * 0.6]);
const elements = Array.from({ length: 5 }, (_, i) => [i, i + 1]);
const loads = new Map([[5, [10, 0, -2000, 0, 0, 0]]]);
const supports = new Map([
  [0, [true, true, true, true, true, true]],
]);
const section = {
  elasticity: 32_836_000, shearModulus: 13_681_666.666666666,
  area: 0.0625, momentInertiaY: 0.00032552,
  momentInertiaZ: 0.00032552, torsionalConstant: 0.000549128125,
};
const elementsProps = new Map(elements.map((_, i) => [i, section]));

try {
  const result = getNlPositionsAndForces(
    nodes, elements, loads, supports, elementsProps,
  );
  const tip = result.positions.slice(15, 18);
  console.log("Tip displacement:", tip.map((x, i) => x - nodes[5][i]));
  console.log("Base element forces:", result.internalForces.get(0));
} catch (error) {
  console.error(error.message);
}

3Inputs and conventions

Indices are zero-based. Use one consistent unit system: with kN and metres, elastic moduli are kN/m², areas m², inertias and torsional constants m⁴, thicknesses m, and moments kN·m. The caller supplies the mesh and converts distributed loads to equivalent nodal loads.

4Optional arguments

getNlPositionsAndForces(
  nodes, elements, loads, supports, elementsProps,
  releases, simSettings, options,
)

releases is an optional Map from frame element index to [My_start, Mz_start, My_end, Mz_end]; true releases that local bending moment. Omit it, or pass undefined, for rigid ends.

simSettings defaults to { tol: 1e-3, maximum_iter: 500 }. If supplying settings, provide both values. options defaults to {} and supports these shell-only features, without releases:

• prescribedTranslations: a Map from node index to [dx, dy, dz]. Values are displacements from the original geometry; null leaves an axis unspecified. A nonzero value cannot conflict with a fixed support.
• shellStress: true: return membraneVonMises, one membrane von Mises stress per input triangle, in the input stress units. This excludes bending and through-thickness stresses.

5Reading results

Invalid input, unsupported topology or failure to converge throws an Error; there is no result.ok flag or partial result. This is an equilibrium solve at the supplied load, not an eigenvalue buckling calculation. A perfectly symmetric model can remain on a symmetric equilibrium; use a suitable geometric imperfection or small lateral load to select a buckling branch, and check mesh convergence.

6Support

Book a call or email mohamed@awatif.co. For a bug report, include a minimal model, solver build and full error message. Results must be independently verified by a qualified engineer before use.