Static (lower-bound) limit analysis of no-tension masonry. Stone is taken as rigid, unable to carry tension, and strong enough in compression; an arch or a dome stands under its own weight if a line of thrust can be drawn entirely inside the masonry (the static, lower-bound theorem of limit analysis). The question each study asks is geometric: how thin can the shape be made before no such line fits?
masonry_lune.py is the rig's solver (plain functions, numpy + scipy/HiGHS):
- a 2-D voussoir arch, or a dome cut into meridional slices with no hoop force (each slice is an arch whose blocks weigh as the exact slice sectors);
- at every joint the resultant must be compressive and lie inside the section:
N >= 0,|M| <= N t / 2, a linear programme in the crown thrust and its moment; - the threshold thickness by bisection, the admissible corridor (the pointwise envelope of the thrust-line eccentricity over every feasible state, two LPs per joint) and the minimum-thrust line.
python -m pip install -r requirements.txt
python reproduce.pyreproduce.py checks the solver against classical values and against reference/rig_reference.json:
| check | this rig | reference value |
|---|---|---|
| semicircular arch, own weight, 160 voussoirs | t/R 0.1074 | 0.1075 (classical) |
| hemispherical dome, slices with no hoop force, 160 blocks per half-slice | t/R 0.04281 | 0.04284 of the mid-surface radius (Nodargi & Bisegna 2021) |
| the same dome with a 12-degree opening at the top | t/R 0.0475 | a different shape gives a different value |
how-thin-a-stone-dome/— an ideal stone hemisphere thinned until its thrust-line corridor is nearly closed, and Gol Gumbaz's reported shell (Cousens 1916) compared with that ideal reference.
Rigid, no-tension blocks that do not slide; own weight; a dome is treated as independent slices (no hoop force). The studies are comparisons of geometry with ideal references, not assessments of any real building.