Research / Optimization

A square gridshell under its own weight

After Helen E. Fairclough, Karol Bołbotowski, Linwei He, Andrew Liew, Matthew Gilbert, “Topology and geometry optimization of grid-shells incorporating design-dependent self-weight loading”, Computers & Structures (2026), doi:10.1016/j.compstruc.2025.107997.

Against the author’s code
11 of 11 checks pass
Against the paper’s figures
1 of 1 checks pass

Research, not a design tool. Nothing here is an engineering result.

One five-node example from Fairclough and colleagues: four supports, one central load, and four curved compression members.

The reproduced example

Table 1, first row: a unit square supported at its four corners, a unit downward load at the centre, unit compressive strength, and normalized unit weight ρgL/σ = 1.65. The ten possible connections form the fixed ground structure. Clarabel solves the second-order cone problem from equations (12)–(18); four connections carry compression. Elevations and equal-stress centrelines are recovered after the solve.

Volume and layout comparison

Published · Table 1
13.8394
Unmodified author reference
13.83937359
Stabileo · Rust / Clarabel
13.83937354

Source: accepted manuscript, printed page 28 (PDF page 29), Table 1. Reference code: Figshare version 1, GPL-3.0-or-later; executed externally and never copied into this repository.

Unmodified author reference

What this establishes

The checks compare volume, active members, forces, centreline coordinates, apex elevation and conic feasibility. The printed volume is checked to half a unit in its last decimal place. Agreement with reference code is not experimental validation or engineering certification.

Production-engine check and editor

The curved result is exported as 128 straight 3D frame segments with circular sections, corner pins, E = 1000 MPa and ν = 0.3. Explicit nodal loads approximate continuous self-weight. The production engine checks linear static response and vertical force balance. Bending stiffness stabilizes this frame surrogate; it is not the paper’s compression-only catenary model. The editor opens this same model. Automatic self-weight is off to avoid counting it twice.

Engine vertical balance · relative error: 0.0000000000137740664

Not yet reproduced

Only the five-node row at this one unit weight is reproduced. The other Table 1 rows, the 11×11 grid, the optimized 13-node layouts, member adding, position search, counterweights, holes, and the full general catenary layout formulation are out of scope. No buckling, nonlinear stability, joints, design checks or experimental validation are claimed.

Questions for the authors

Can you confirm the canonical Table 1 inputs and solver tolerances, recommend an open-solver configuration, and advise how to export sections and centrelines for independent stability analysis?

Cite this

Stabileo Research, “A square gridshell under its own weight”, reproduction of Helen E. Fairclough, Karol Bołbotowski, Linwei He, Andrew Liew, Matthew Gilbert (2026), doi:10.1016/j.compstruc.2025.107997. Implementation: research/optimisation/fairclough-2026 at commit 8068cd16ea2c. Engine: the Stabileo engine at the same commit. Permanent links to this exact build are planned.