Discretisation error
Span 10 · unstretched length 12 · w = 1 · EA = 10,000 · level supports, dimensionless throughout.
Maximum node distance from the exact curve at the same unstretched arc length, si = iL0/n.
| Segments | Max error | H error | Iterations |
|---|
Timber gridshell
A hanging net finds its own shape under its own weight. Move a support and watch the net settle, then turn it upside down to get a compression shell and see how sharply its laths must bend.
It follows a long line of hanging models, from Gaudí and Isler to Frei Otto’s Mannheim gridshell.
Compression shell / mirrored equilibrium
Lath curvature, 1/R
0, gentletight
Equal unstretched links, two lath directions, no diagonals.
Drag a ring, or select a support and use the arrows.
Finding equilibrium…
- Iterations
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- Residual / weight
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- Converged?
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- Rise / base span
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- Max |force| / weight
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- Link force sign
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Tightest radius —
Illustrative bending stress —
How hard the laths are being bent: σ = E·t/(2R), using E = 11,000 N/mm² and an assumed 10 m base span to give the dimensionless form a scale. This is an illustration, with no strength limit or design verdict. Colour shows curvature, not force.
Orbit with a mouse drag or horizontal touch drag.
With the 3-D view focused, arrow keys orbit and Home restores the view. With the plan focused, arrow keys move the selected support.
Support movement is limited to 15% of the base span per plan axis about its original position.
This is not a design.
Method and limits
A form illustration. A genuine numerical check.
The net is a pin-jointed, linearly elastic axial-link model. Its links start with equal unstretched length, and a high axial stiffness makes them nearly inextensible. The grid can shear because it has no diagonals. Support dragging starts the next relaxation from the last shape. Links joining two fixed supports can remain compressed when their end spacing is shorter than their rest length; the force-sign readout retains this.
The shell is the hanging shape mirrored vertically, with every axial force reversed: tension becomes compression. This is the ideal funicular analogy under the same downward nodal loads, not a separate elastic shell analysis. Mirroring preserves link lengths; reversed forces would require different stress-free lengths. Curvature is estimated from the circle through three successive nodes along each lath.
There is no material nonlinearity, lath bending stiffness in the form-finding, buckling, wind, snow, connection design or safety factor. The curvature estimate and the convergence PASS are not structural design checks.
The model checks itself
Refining a gridshell mesh changes the structure: more grid lines mean more laths. It is not a convergence study. A hanging chain does have a continuum limit, so the same relaxation solver is tested against the closed-form elastic catenary.
Computing the chain study locally…
Iteration error
The current net’s out-of-balance force at its worst free node, divided by total weight, updated after every change.
Convergence means r < 10⁻⁶. A small residual establishes equilibrium of this pin-jointed model; it does not establish the adequacy of a shell.
r = maxi |Fi| / Σ(w·l0)
T = EA(l − l0)/l0
Self-weight per unstretched length is split equally between each link’s ends, including the load carried directly at supports. Links can carry either force sign. Kinetic damping removes fictitious motion as the net settles.
A line to check on paper.
Calculating the continuum solution…
q(s) = w·s − VA
x(s) = H/w [asinh(q/H) − asinh(−VA/H)] + Hs/EA
z(s) = [√(H² + q²) − √(H² + VA²)]/w + (ws²/2 − VA·s)/EA
x(L0) = span; z(L0) = dz; VB = wL0 − VA
H and VA satisfy the two support coordinates. Reference: Irvine, Cable Structures (1981), elastic catenary under uniform load per unstretched length. Relaxation follows the kinetic-damping approach of Barnes. Before publication, three chain cases (level and inclined, stiff and stretchy) were solved blind from first principles as a separate reference; this solver agreed with that reference to within 2 × 10⁻⁹.