SP-8007 Data Handoff

Tensyl can prepare equivalent stiffness-property data for a separate SP-8007-style or orthotropic-cylinder calculation. Tensyl does not compute SP-8007 knockdown factors, buckling loads, margins, or allowables. Its job here is narrower: compute and preserve local equivalent ABD stiffness data, geometry context, validity ratios, assumptions, and serialized artifacts for another calculation to consume.

NASA SP-8007 is shell-buckling guidance. Nemeth's equivalent-plate work is a source for stiffened equivalent-plate stiffness concepts. Tensyl sits between those worlds: it produces local stiffness data, then gets out of the way.

Treat an SP-8007 handoff as a translation, not as proof that either model is right. The barred constants below are the data shape expected by a classical orthotropic-cylinder calculation. They are useful precisely because they are small and familiar, but that also means they can hide terms that are present in the full ABD stiffness. The public SP-8007 reconciliation report shows where Tensyl and the SP-8007 elastic-constant formulas agree, and where they diverge because the models retain different bending physics. That report also calls out a printed-equation problem in SP-8007: isogrid Eqs. 97-98 omit the explicit eccentric EA z^2 bending terms. Correct that omission before using the isogrid bending formulas as a physics reference.

A downstream SP-8007-style workflow commonly needs these data categories from a stiffness model:

• SP-8007 orthotropic-cylinder extensional coefficients Ebar_x, Ebar_y, Ebar_xy, and Gbar_xy;
• bending and twisting coefficients Dbar_x, Dbar_y, and Dbar_xy;
• membrane-bending coupling coefficients Cbar_x, Cbar_y, Cbar_xy, and Kbar_xy when coupling is not negligible;
• transverse-shear stiffnesses As when relevant;
• whether membrane-bending coupling B is negligible or must be retained;
• cylinder radius and length from geometry;
• pitch, stiffener height, and validity ratios such as h_over_R, p_over_R, and p_over_L_response;
• warnings, assumptions, and serialized artifacts for traceability.

Coefficient Extraction

For the built-in Cylinder, Tensyl's local e1 direction is axial and local e2 is circumferential. Under the SP-8007 Section 4.1.2 orthotropic-cylinder assumption that the orthotropy axes coincide with those directions, the barred coefficients used in Eqs. 54-59 and 71-81 map to Tensyl's local ABD stiffness as:

Dbar_xy is not just D[2, 2]. It is the modified twisting coefficient: the combined bending-twist term used by classical orthotropic shell equations when they collapse the bending block into a smaller coefficient set. Tensyl's public strain convention uses engineering shear/twist ordering (e11, e22, gamma12, k11, k22, k12, gamma13, gamma23), so the coefficient is 2*D12 + 4*D66.

For stiffened walls, pay special attention to Dbar_x, Dbar_y, and Dbar_xy. Tensyl retains centroidal beam-section terms through the member strain map. Some SP-8007 elastic-constant expressions omit beam contributions that Tensyl includes. When those numbers disagree, inspect section inertia, torsion constant, reference-surface choice, and eccentricity.

For orthogrids, the main known reduction is cross-family in-plane bending. Tensyl includes rib EIz in Dbar_x and stringer EIz in Dbar_y. SP-8007 ring/stringer Eqs. 89-91 do not expose those terms, so a handoff that keeps only the barred constants can hide bending stiffness from wide, flanged, capped, or closed stiffeners.

For isogrids with eccentric members, use corrected bending terms:

and

Use orthotropic_coefficients() when a downstream hand calculation wants this smaller coefficient set:

coefficients = result.orthotropic_coefficients()

print(coefficients.Ebar_x, coefficients.Dbar_x, coefficients.Dbar_xy)
print(coefficients.warnings)
print(coefficients.unsupported_terms)

Orthogrid Handoff

This worked handoff prepares an orthogrid equivalent stiffness for a separate SP-8007-style cylinder workflow.

from tensyl import (
    BeamSection,
    Cylinder,
    EnergyHomogenizer,
    IsotropicMaterial,
    ValidityContext,
    isotropic_plate,
    orthogrid_cell,
)
from tensyl.io import from_yaml, to_yaml


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,
    ),
)
surface = Cylinder(radius=120.0, length=300.0)
point = surface.point_at(150.0, 0.0)
sp8007 = result.orthotropic_coefficients()

report = {
    "radius": surface.radius,
    "length": surface.length,
    "sp8007": sp8007,
    "transverse_shear": {
        "Abar_xz": result.stiffness.As[0, 0],
        "Abar_yz": result.stiffness.As[1, 1],
    },
    "h_over_R": result.validity.h_over_R,
    "p_over_R": result.validity.p_over_R,
    "p_over_L_response": result.validity.p_over_L_response,
    "warnings": result.validity.warnings,
    "assumptions": result.assumptions,
    "frame_label": point.frame.label,
}

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

assert loaded.stiffness.C8.shape == (8, 8)
assert report["sp8007"].Ebar_x == result.stiffness.A[0, 0]
assert report["sp8007"].Dbar_xy == 2.0 * result.stiffness.D[0, 1] + 4.0 * result.stiffness.D[2, 2]
assert report["p_over_R"] == 8.0 / 120.0

Use the serialized artifact as a traceable record of the stiffness-property calculation. Unit labels are metadata; Tensyl does not convert values.

Isogrid Variant

For an equilateral isogrid whose local 0 degree member family is axial, extract the same SP-8007 coefficient set from the homogenized ABD stiffness:

from tensyl import equilateral_isogrid_cell


isogrid_skin = isotropic_plate(
    IsotropicMaterial(E=10.6e6, nu=0.33, density=0.1),
    thickness=0.060,
)
isogrid_section = BeamSection(
    EA=2.8e6,
    EIy=1.8e4,
    EIz=5.2e3,
    GJ=3.2e3,
    kGAy=0.9e6,
    kGAz=0.7e6,
)
isogrid_cell = equilateral_isogrid_cell(
    skin=isogrid_skin,
    member_section=isogrid_section,
    pitch=6.0,
    eccentricity=0.35,
)
isogrid_result = EnergyHomogenizer().compute(
    isogrid_cell,
    validity_context=ValidityContext(
        characteristic_height=0.42,
        pitch=6.0,
        min_radius=120.0,
        response_length=80.0,
    ),
)
isogrid_sp8007 = isogrid_result.orthotropic_coefficients()

assert abs(isogrid_sp8007.Ebar_x - isogrid_sp8007.Ebar_y) < 1.0e-6
assert abs(isogrid_sp8007.Cbar_x - isogrid_sp8007.Cbar_y) < 1.0e-6

The equality checks are not SP-8007 requirements. They are useful sanity checks for this equilateral, equal-member example because the isogrid should be balanced in the local axial and circumferential directions.

Symmetric Laminate Variant

For a skin-only laminate cylinder, build the laminate ABD stiffness directly and extract the same barred coefficients. This example uses a symmetric cross-ply stack so the membrane-bending coupling block is negligible.

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,
)
laminate_stiffness = laminate_plate(
    (
        Ply(material=carbon_epoxy, thickness=0.005, angle_rad=0.0),
        Ply(material=carbon_epoxy, thickness=0.005, angle_rad=1.5707963267948966),
        Ply(material=carbon_epoxy, thickness=0.005, angle_rad=1.5707963267948966),
        Ply(material=carbon_epoxy, thickness=0.005, angle_rad=0.0),
    )
)
laminate_sp8007 = laminate_stiffness.orthotropic_coefficients()
laminate_report = {
    "radius": surface.radius,
    "length": surface.length,
    "sp8007": laminate_sp8007,
    "transverse_shear": {
        "Abar_xz": laminate_stiffness.As[0, 0],
        "Abar_yz": laminate_stiffness.As[1, 1],
    },
}

assert abs(laminate_report["sp8007"].Cbar_x) < 1.0e-9
assert abs(laminate_report["sp8007"].Cbar_y) < 1.0e-9