Sectalix

Sectalix is a Python library and command-line tool for thin-walled structural cross-sections. It evaluates closed-form centerline integrals in float64 for open, closed (multi-cell), and mixed topologies, without numerical quadrature or finite element meshing.

Key Features

• Exact Analytical Integrals: Closed-form line integrals for cross-sectional area $A$, centroid $C=(x_c, y_c)$, second moments of area ($I_x, I_y, I_{xy}$), principal properties ($I_1, I_2, \theta_p$), and Saint-Venant torsion constant $J$.
• Shear Flow & Shear Center: Tree-equilibrium transverse shear flow for open sections, Bredt-Batho compatibility circulations for multi-cell closed sections, and shear center $S=(x_s, y_s)$ determination.
• Vlasov Warping Theory: Continuous sectorial coordinate field $\omega^\ast(s)$ with zero-mean normalization and sectorial warping constant $C_w$.
• Stress Recovery & Peak Search: Analytical stress profiles ($\sigma_{zz}, \tau_{\rm surface}, \sigma_{\rm vm}$) with polynomial root-finding for peak von Mises stress and elastic first-yield multiplier ($\lambda$), rather than sampled peak estimation.
• Zero Heavy Dependencies: Core computation runs strictly on Python standard library and numpy. Plotting optionally utilizes matplotlib.
• Engineering CLI & Calculation Sheets: Built-in command line interface (sectalix) with standard UNIX exit codes, streaming piping (stdin/stdout), and automated GitHub-Flavored Markdown Calculation Sheet generator.
• CAD & Lossless Interchange: Exact IEEE-754 float64 hexadecimal JSON serialization and standalone ASCII DXF importer.

Installation

From PyPI

python -m pip install sectalix

From Source / Clone

git clone https://github.com/bboranozdemir-lgtm/Sectalix.git
cd Sectalix
pip install -e .

To enable headless visualization and technical plot generation:

pip install -e ".[plots]"

Quickstart

1. Command-Line Interface (CLI)

Sectalix provides a unified CLI for inspecting sections, converting CAD files, and solving stress recovery:

# Inspect cross-section characteristics (Area, Centroid, Inertia, J, Cw)
sectalix inspect examples/sample_sections/rectangle.dxf

# Run full stress recovery analysis under external loads
sectalix analyze examples/sample_sections/rectangle.dxf \
  --N 10000 --Vy 5000 --Mx 250000 --sigma-yield 355 \
  --report calculation_report.md \
  --plots-dir ./output_plots

# Directly render section geometry to PNG/SVG
sectalix plot examples/sample_sections/rectangle.dxf --output geometry.png

The rectangle example is a 4 x 2 mm centerline box with thickness 0.01 mm, encoded by its THICK_0.01 DXF layer. The CLI --thickness option is only a fallback for entities without mapped thickness; it does not override that layer. These small sample dimensions demonstrate the interface, not a practical design. Plot-producing commands require the optional plots installation above.

2. Python API

from sectalix import Node, Segment, Section, AppliedLoads

# Define an open channel section (C-Channel: 50x100x50 mm, t=2 mm)
n0 = Node(x=50.0, y=100.0)
n1 = Node(x=0.0, y=100.0)
n2 = Node(x=0.0, y=0.0)
n3 = Node(x=50.0, y=0.0)

section = Section([
    Segment(p1=n0, p2=n1, t=2.0),
    Segment(p1=n1, p2=n2, t=2.0),
    Segment(p1=n2, p2=n3, t=2.0),
])

# Access geometric & torsional properties
print(f"Area: A = {section.area:.2f} mm^2")
print(f"Centroid: C = ({section.cx:.2f}, {section.cy:.2f}) mm")
print(f"Inertia: Ix = {section.Ix:.2f}, Iy = {section.Iy:.2f} mm^4")
print(f"Saint-Venant Torsion: J = {section.J:.2f} mm^4")
print(f"Warping Constant: Cw = {section.Cw:.2f} mm^6")

# Recover stresses under combined loads (Axial + Shear + Bending)
loads = AppliedLoads(N=10000.0, Vy=5000.0, Mx=250000.0, sigma_yield=355.0)
results = section.calculate_stresses(loads)

print(f"Peak Von Mises: {results.max_sigma_vm:.2f} MPa")
print(f"Elastic Load Factor: lambda = {results.load_factor:.3f}")

Topology & Capabilities Matrix

Engineering Assumptions & Scope

• Thin-Wall Centerline Model: Geometry is represented by 1D straight segments along wall centerlines with uniform segment thickness $t$.
• Omitted Effects: Corner fillets, root radii, and local corner overlap volumes are neglected. Plate through-thickness transverse shear deformation is omitted.
• Elastic Scope: Sectalix calculates linear-elastic section properties and stress distributions. It does not perform plastic hinge analysis, local/global buckling verification, or structural design code checks (AISC/Eurocode). The elastic load factor is a first-yield indicator, not a regulatory safety certification.

Documentation

• Theory & Conventions: Complete mathematical derivations, coordinate frames, right-hand rules, and sign conventions.
• CLI Reference: Comprehensive guide to CLI subcommands, options, piping, and exit codes.
• Verification Benchmarks: Summary of analytical and independent oracle benchmarks.
• Developer Guide: Development setup, repository architecture, and contributor rules.
• Release & PyPI Guide: Distribution packaging and release procedures.

License

Sectalix is released under the MIT License.