Beam Design Optimiser

An engineering design-optimisation program in Python. It finds the lightest (or cheapest) solid rectangular beam that still meets a set of requirements — allowable deflection, a safety factor on yield stress, and an optional mass cap. It searches thousands of width/height combinations, picks the best feasible one, draws the trade-off graphs, and writes a full engineering report.

I built it to practise the difference between analysing a design and optimising one: searching a design space against constraints, and being explicit about the assumptions behind the answer.

• Four load cases: simply-supported or cantilever, point load or UDL
• Five materials with real properties (E, yield, density, cost): 6061-T6 and 7075-T6 aluminium, S275 and S355 steel, Ti-6Al-4V
• Optimise for mass or cost
• Includes the beam's own self-weight in the load (can be switched off)
• Coarse grid search followed by a refinement pass around the optimum
• Outputs four graphs and a Markdown engineering report

pip install -r requirements.txt

Python 3.10+ with numpy and matplotlib.

Built-in demo (2.0 m simply-supported aluminium beam, 5 kN point load):

python main.py --demo

Custom design brief:

python main.py --length 2.0 --load 5000 --material aluminium_6061_t6 \
    --max-deflection 8 --safety-factor 2.0 --load-case ss_point

=== OPTIMUM DESIGN ===
  width  b = 13.77 mm
  height h = 109.99 mm
  mass     = 8.180 kg   cost = GBP 28.63
  deflection = 8.00 mm (limit 8.00 mm)     <- deflection-limited
  safety factor = 3.04 (required 2.00)

The optimum sits exactly on the deflection limit, with stress well inside yield — so for this brief the beam is stiffness-driven, not strength-driven. The design-space plot above shows why: the optimum is on the boundary of the feasible region, at the lowest-mass point that still clears the deflection line.

Written to output/ (or --outdir):

• design_space.png — every candidate, the feasible region and the optimum
• height_vs_mass.png — section height vs mass at the optimum width
• height_vs_deflection.png — section height vs deflection, with the limit line
• mass_vs_deflection.png — the mass-vs-stiffness trade-off for feasible designs
• engineering_report.md — assumptions, equations, inputs, results, limitations

Euler–Bernoulli bending of a prismatic solid rectangular section:

I = b·h³/12         Z = b·h²/6
M_max = k_m·F·L      δ = k_d·F·L³/(E·I)
σ = M_max/Z          n = σ_y/σ          m = ρ·b·h·L

Load-case coefficients (k_m, k_d):

• Optimisation thinking — framing a design problem as an objective plus constraints, and reading the answer off the boundary of the feasible region.
• Structural mechanics — bending stress, deflection and where the standard beam formulae come from, including the effect of the beam's own weight.
• Being explicit about assumptions — the auto-generated report forces every simplification (linear-elastic, small deflection, no buckling or shear) to be written down next to the result.
• Modular code — separating the mechanics, the search, the plotting and the reporting so each part can be checked on its own.

Skills: Python · NumPy · Matplotlib · structural mechanics · optimisation · technical report writing · Git

Educational conceptual tool — solid rectangular sections only, no buckling, shear, fatigue or code checks. Not for actual structural design.