How much does a bolt hole cost a tension plate, and which rule sets its width?

What it found

A flat plate carrying one required hole is sized for minimum mass under a working-stress limit with three stress models (net section, a fixed Kt = 3, and 2D finite elements over d/W) and with per-process hole rules (minimum hole, centre-to-edge distance, ligament, stock thickness). FE reproduces the large-plate limit of Kt = 3 as the hole shrinks. Ignoring the concentration gives plates 1.9–2.7× overstressed where stress binds; Kt = 3 is safe but 8–26% heavier for FDM. Where an edge-distance rule binds (CNC routing, laser from 8 mm, casting from 8 mm) the stress model is irrelevant and the plate is 2–4× stronger than needed. Stylised: rule values, load and materials are assumed, 2D plane stress, no bolt contact or fatigue, mesh not fully converged (about 1% low), nothing built.

A figure from its own output

Paper, code and results

• README and method
• Experiments and results
• Code
• Tests

More in Simulation-first design

• Does weighting parts by mass change which shop process, and which machine, matters?Does weighting parts by mass change which shop process, and which machine, matters? With a tip load FDM covers 0.30 of parts by count and 0.58 by mass, the laser-versus-CNC order flips, and at budgets 600–800 exhaustive search picks the laser cutter by count but the casting setup by mass (one seed). Stylised, assumed rules and prices, simulated only.
• Do the mass-weighting machine-choice flips of simdesign-coverweight survive across seeds?Do the mass-weighting machine-choice flips of simdesign-coverweight survive across seeds? Over 20 seeds, log flips from the laser cutter (count) to the casting setup (mass) in 20/20 at budgets 600–800, large only at 800, small never; the 1100–1400 flips are near-ties (≤0.26 points). Stylised, assumed rules and prices, simulated only.
• How wide are the budget bands where mass weighting changes the machine choice when prices are uncertain?How wide are the budget bands where mass weighting changes the machine choice when prices are uncertain? With ±20% independent price noise the log flip band widens from budgets 600–800 to 500–1000 but softens at its edges (about one half), and large's single nominal flip at 800 shows up in only 44% of price draws. Stylised, assumed rules and prices, simulated only.
• Which share of a bracket family can each shop process make, and which machine should a shop add next?Share of a sampled bracket family each shop process can make under the simdesign-dfm rules: geometry alone adds nothing beyond FDM (negative), with a tip-load requirement the processes separate (FDM alone 30%, +casting +laser 41%) and the best next machine depends on budget and part size, where greedy sometimes loses 1–2 points to exhaustive search (stylised, assumed rules).
• Does a mesh-aware stress margin change what manufacturing rules cost a sized bracket?Re-runs simdesign-dfm with a stress knock-down and a finer search mesh, checking designs at h = 0.7 mm: the price ordering (casting ~1.4, CNC ~1.23, FDM 1.0) survives the mesh, the laser-cutting price does not (1.01–1.22, noisy), and a 1.3 margin leaves designs at 0.88–1.02 of the limit (stylised, assumed rule values).
• Does a patch-averaged stress converge under mesh refinement where the peak element stress does not?Compares peak and patch-averaged von Mises stress under mesh refinement on the L-bracket: the peak rises 18–41% from h = 2.5 to 0.55 mm while a 3 mm patch average moves 1–6%, but it reads only 0.45–0.69 of the peak so needs its own limit (stylised, assumed values).

All 64 Simulation-first design projects →

Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.