tensyl 0.2.1

Equivalent-stiffness homogenization for stiffened plates and shells.

Tensyl

Tensyl is a Python scientific-computing library for equivalent-stiffness homogenization of stiffened plates and shells.

The library builds local ABD and transverse-shear stiffness laws for skins, laminates, stiffened tangent-plane cells, and geometry-bound stiffness fields. It keeps conventions, diagnostics, validity data, and serialization metadata explicit.

The public Python package name is tensyl.

Mechanics Lineage

Tensyl implements a documented equivalent-plate tradition in Python. The first stiffened-cell homogenization family is based on Michael P. Nemeth's NASA treatise, A Treatise on Equivalent-Plate Stiffnesses for Stiffened Laminated-Composite Plates and Plate-Like Lattices (NASA/TP-2011-216882), which collects direct equilibrium-compatibility and strain-energy formulations for stiffened laminated plates and plate-like lattices.

The stiffness notation follows classical laminated plate and first-order shear-deformation theory: A, B, D, and As are stored together as one canonical 8 x 8 tangent. The documentation lists the mechanics sources in References and writes out the governing equations in Equivalent-Stiffness Mechanics.

Install

uv add tensyl

or:

pip install tensyl

For local development from this repository:

uv sync --dev

Library Capabilities

Materials and skins

• isotropic plate skins with transverse shear;
• orthotropic ply materials;
• bottom-to-top laminate stacks with ply angle, thickness, and density;
• canonical A, B, D, As, and C8 stiffness storage.

Stiffener sections

• direct BeamSection input for EA, EI, GJ, and shear stiffness products;
• geometry-derived open thin-wall sections for blade, tee, zee, channel, and hat stiffeners;
• custom ThinWallSegment layouts for open thin-wall section geometry.

Cell and pattern libraries

• unidirectional and orthogrid cells;
• braced orthogrid cells;
• equilateral isogrid cells;
• isosceles triangle, Kagome, hexagonal, and star pattern cells;
• sandwich-core variants;
• graph-defined custom unit cells through CellNode, CellEdge, and graph_unit_cell.

Homogenization and review data

• EnergyHomogenizer as the reference homogenizer;
• DirectECHomogenizer for supported direct equilibrium-compatibility cases;
• HomogenizationResult with stiffness, diagnostics, assumptions, and validity;
• scale-separation checks for stiffener height, pitch, curvature radius, response length, and membrane-bending coupling.

Geometry and fields

• flat plates, cylinders, spheres, spherical caps, conical frustums, and ellipsoids;
• constant stiffness fields;
• pointwise homogenized stiffness fields with local cell factories;
• sampled stiffness atlases with bilinear interpolation in canonical C8 storage.

External handoff

• YAML and JSON serialization for ABDStiffness and HomogenizationResult;
• schema versioning, unit labels, diagnostics, assumptions, and validity metadata;
• solver-neutral artifacts for downstream tools.

Example 1: Skin-Only ABD Stiffness

An isotropic skin about its mid-surface has zero membrane-bending coupling in the B block.

from tensyl import IsotropicMaterial, isotropic_plate

aluminum = IsotropicMaterial(E=10.6e6, nu=0.33, density=0.1)
stiffness = isotropic_plate(aluminum, thickness=0.080)

print(stiffness.A)   # membrane stiffness
print(stiffness.B)   # membrane-bending coupling
print(stiffness.D)   # bending stiffness
print(stiffness.As)  # transverse-shear stiffness

The canonical tangent is an 8 x 8 matrix. The named blocks are views into that operator:

• A: membrane stiffness;
• B: membrane-bending coupling;
• D: bending and twisting stiffness;
• As: transverse-shear stiffness.

Tensyl keeps stiffness as the first-class result. Scalar equivalent moduli are derived interpretations, not the primary object.

Example 2: Composite Laminate

laminate_plate builds a plate stiffness from ply material, ply thickness, and ply angle. The stack is supplied bottom-to-top.

import math

from tensyl import OrthotropicPlyMaterial, Ply, laminate_plate

carbon_epoxy = OrthotropicPlyMaterial(
    E1=18.0e6,
    E2=1.4e6,
    G12=0.75e6,
    nu12=0.28,
    G13=0.75e6,
    G23=0.50e6,
    density=0.058,
)

stiffness = laminate_plate(
    (
        Ply(material=carbon_epoxy, thickness=0.005, angle_rad=0.0),
        Ply(material=carbon_epoxy, thickness=0.005, angle_rad=0.5 * math.pi),
        Ply(material=carbon_epoxy, thickness=0.005, angle_rad=0.0),
    )
)

assert stiffness.C8.shape == (8, 8)
assert abs(stiffness.B).max() < 1.0e-9

The two zero-degree plies make the local e1 direction stiffer than e2. The symmetric stack keeps B near zero, so membrane strain and bending curvature are not coupled by the chosen reference surface.

Example 3: Geometry-Derived Orthogrid

Thin-wall section helpers compute centroidal beam-section stiffnesses from section geometry. Those sections can be used directly in cell constructors.

from tensyl import (
    EnergyHomogenizer,
    IsotropicMaterial,
    blade_section,
    hat_section,
    isotropic_plate,
    orthogrid_cell,
)

aluminum = IsotropicMaterial(E=10.6e6, nu=0.33, density=0.1)
skin_thickness = 0.080
skin = isotropic_plate(aluminum, thickness=skin_thickness)

stringer = hat_section(
    material=aluminum,
    web_height=0.50,
    web_thickness=0.050,
    crown_width=0.40,
    crown_thickness=0.050,
    flange_width=0.20,
    flange_thickness=0.050,
)

rib = blade_section(
    material=aluminum,
    height=0.50,
    thickness=0.050,
    shear_correction_y=5.0 / 6.0,
    shear_correction_z=5.0 / 6.0,
)

skin_face_offset = 0.5 * skin_thickness
cell = orthogrid_cell(
    skin=skin,
    stringer_section=stringer.section,
    rib_section=rib.section,
    stringer_spacing=6.0,
    rib_spacing=8.0,
    stringer_eccentricity=skin_face_offset + stringer.centroid_z,
    rib_eccentricity=skin_face_offset + rib.centroid_z,
)

result = EnergyHomogenizer().compute(cell)

print(result.stiffness.A)
print(result.stiffness.B)
print(result.diagnostics)
print(result.validity.warnings)

The result contains the homogenized stiffness, diagnostics, modeling assumptions, and validity warnings. Nonzero B follows from eccentric stiffeners relative to the chosen reference surface.

Example 4: Custom Graph Cell

graph_unit_cell defines a tangent-plane cell from local nodes, edges, section properties, eccentricities, and cell area.

from tensyl import (
    BeamSection,
    CellEdge,
    CellNode,
    EnergyHomogenizer,
    graph_unit_cell,
)

section = BeamSection(
    EA=3.2e6,
    EIy=2.4e4,
    EIz=6.5e3,
    GJ=4.0e3,
    kGAy=1.1e6,
    kGAz=0.9e6,
)

custom = graph_unit_cell(
    area=48.0,
    skin=skin,
    nodes=(
        CellNode(0.0, 0.0),
        CellNode(6.0, 0.0),
        CellNode(0.0, 8.0),
    ),
    edges=(
        CellEdge(0, 1, section, eccentricity=0.45),
        CellEdge(0, 2, section, eccentricity=0.45),
    ),
)

custom_result = EnergyHomogenizer().compute(custom)

The graph constructor converts the node and edge layout into canonical beam members before homogenization.

Example 5: Stiffness on a Shell Surface

Geometry is separate from constitutive stiffness. A cylinder supplies local frames and curvature context; it does not alter the numeric ABD matrix in a constant stiffness field.

from tensyl import ConstantStiffnessField, Cylinder

surface = Cylinder(radius=120.0, length=300.0)
field = ConstantStiffnessField(result.stiffness)

stiffness_at_midbay = field.stiffness_at(surface, 150.0, 0.0)

assert stiffness_at_midbay.frame.label == "cylinder"
assert stiffness_at_midbay.C8.shape == (8, 8)

Variable structure can be represented with HomogenizedStiffnessField, which rebuilds the local cell at each surface point, or with ABDAtlas, which interpolates sampled stiffnesses.

Example 6: Export

tensyl.io serializes stiffnesses and homogenization results to solver-neutral YAML or JSON artifacts.

from pathlib import Path

from tensyl.io import read_yaml, to_yaml, write_yaml

text = to_yaml(
    result,
    units={"length": "in", "force": "lbf", "stress": "psi"},
)

write_yaml(
    result,
    Path("stiffness.yaml"),
    units={"length": "in", "force": "lbf", "stress": "psi"},
)

same_result = read_yaml(Path("stiffness.yaml"))

Unit labels ride along with the export as metadata; Tensyl never inspects or converts the values. Whatever consistent system you put in is the system you get back.

Scope

Tensyl forms and audits equivalent ABD stiffnesses. It is not a certification buckling solver, a local stress recovery tool, or a substitute for detailed finite-element analysis, and its tangent-plane homogenization relies on scale separation between stiffener pitch, stiffener height, local curvature radius, and the structural response length of interest.

Local buckling, crippling, joints, cutouts, load introduction, nonlinear postbuckling, and final allowables stay outside the current package scope.

Documentation Map

The formal documentation is built with MkDocs from docs/.

• Getting started covers setup and the shortest path to an ABD stiffness.
• Background explains the engineering motivation and terminology.
• Theory documents ABD stiffnesses, conventions, tangent-plane homogenization, and validity limits.
• User guide covers materials, cells, sections, geometry, fields, and external handoff.
• Examples provides worked examples and executable snippets.
• API reference exposes the public Python interfaces.
• References lists the external sources used by the mechanics documentation.

Development

This repository uses uv for dependency management and command execution.

uv sync --dev
uv run ruff check .
uv run ruff format --check .
uv run ty check
uv run pytest
uv run mkdocs build --strict

Release notes are tracked in CHANGELOG.md, and contribution process details are in CONTRIBUTING.md.

Documentation Authoring

Documentation math uses $...$ for inline equations and $$...$$ for display equations so the same Markdown renders in Obsidian and MkDocs.