Orthogrid Panel and Barrel

This example adds stiffeners to the skin, computes a homogenized ABD stiffness, and attaches the result to a cylindrical midsurface. The numbers are illustrative, not allowables.

Orthogrid Panel

Build an orthogrid panel about the skin reference surface. Stringers run along local e1; ribs run along local e2. Both stiffener families are external to the +n side of the skin reference surface, so positive eccentricity should create membrane-bending coupling.

from tensyl import (
    BeamSection,
    EnergyHomogenizer,
    IsotropicMaterial,
    ValidityContext,
    isotropic_plate,
    orthogrid_cell,
)

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

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

cell = orthogrid_cell(
    skin=skin,
    stringer_section=section,
    rib_section=section,
    stringer_spacing=6.0,
    rib_spacing=8.0,
    stringer_eccentricity=0.45,
    rib_eccentricity=0.45,
)

result = EnergyHomogenizer().compute(
    cell,
    validity_context=ValidityContext(
        characteristic_height=0.50,
        pitch=8.0,
        min_radius=120.0,
        response_length=80.0,
    ),
)

stiffness = result.stiffness

assert stiffness.C8.shape == (8, 8)
assert result.diagnostics["symmetric"]
assert result.diagnostics["positive_semidefinite"]
assert stiffness.B[0, 0] > 0.0

Review result.validity.warnings before using the ABD stiffness downstream.

Selected Output

These inputs match the walkthrough in Homogenization and Results, so the blocks come out the same; that page reads them term by term.

Rounded diagonal values:

Block	Diagonal values
A	1.485e6, 1.352e6, 3.990e5 lbf/in
B	2.400e5, 1.800e5, -3.609e4 lbf
D	1.133e5, 8.559e4, 1.670e4 lbf*in
As	4.157e5, 3.782e5 lbf/in

Interpretation

The diagonal A terms show membrane stiffness added by the grid. Nonzero B comes from eccentric stiffeners relative to the reference surface. Diagnostics confirm the assembled tangent is symmetric and positive semidefinite for this model; they do not prove local stiffener strength, crippling resistance, or a shell buckling margin.

Constant-Stiffness Barrel

Attach the same orthogrid stiffness to a cylindrical midsurface. This binds the constant C8 tangent to the cylinder frame at the requested point; it does not recompute the local stiffened cell.

from tensyl import ConstantStiffnessField, Cylinder

radius = 120.0
surface = Cylinder(radius=radius, 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)
assert result.validity.p_over_R == 8.0 / radius

For Cylinder, e1 is axial, e2 is circumferential, and n points outward. The orthogrid constructor maps stringers to e1 and ribs to e2.

The barrel radius enters the validity ratio p_over_R; it does not recalculate the local orthogrid stiffness. This is still stiffness-property preparation. Loads, boundary conditions, knockdown factors, and buckling margins belong to a separate workflow.