Homogenization and Results

The reference homogenizer is EnergyHomogenizer. It computes a local equivalent ABD stiffness for a canonical tangent-plane unit cell.

from tensyl import EnergyHomogenizer

result = EnergyHomogenizer().compute(cell)
stiffness = result.stiffness

result.stiffness is an ABDStiffness. The same validity report is attached to stiffness.validity, so warnings travel with the ABD stiffness when it is passed to later workflow steps.

Use the result object first. It contains the ABD stiffness and the context needed to judge the calculation:

• result.stiffness.A, B, D, and As are the stiffness blocks;
• result.diagnostics reports numerical checks such as symmetry, rank, and positive-semidefinite status;
• result.assumptions records modeling assumptions;
• result.validity.warnings reports scale-separation and coupling warnings.

Direct Equilibrium-Compatibility

DirectECHomogenizer supports straight stiffener-family inputs where the direct method is applicable.

from tensyl import DirectECHomogenizer

result = DirectECHomogenizer().compute(cell)

Use the direct method as a supported comparison or accelerator, not as a more general replacement for the energy method.

Reading the Result

HomogenizationResult is the main object to inspect after computing a stiffened ABD stiffness.

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,
    ),
)

print(result.stiffness.A)
print(result.stiffness.B)
print(result.stiffness.D)
print(result.stiffness.As)
print(result.diagnostics)
print(result.assumptions)
print(result.validity.warnings)

Selected output, rounded:

Item	Value
A11, A22, A66	1.485e6, 1.352e6, 3.990e5 lbf/in
B11, B22, B66	2.400e5, 1.800e5, -3.609e4 lbf
D11, D22, D66	1.133e5, 8.559e4, 1.670e4 lbf*in
As11, As22	4.157e5, 3.782e5 lbf/in
diagnostics	symmetric, positive-semidefinite, rank 8
warnings	p_over_R_exceeds_threshold, p_over_L_response_exceeds_threshold, membrane_bending_coupling_exceeds_threshold

For SI inputs the same blocks have units N/m, N, N*m, and N/m, respectively. Tensyl preserves whichever system you feed it (see Units and Consistency); it never converts.

Reading the Blocks

• A controls membrane force response.
• B couples membrane strain to bending resultants and curvature to membrane resultants.
• D controls bending and twisting moment response.
• As controls transverse-shear resultants.

A symmetric tangent is required for an energy-based linear stiffness. A positive-semidefinite tangent means the assembled stiffness has no negative-energy mode at the tested tolerance. A rank-deficient tangent means some generalized strain mode is unsupported by the modeled skin and members; Tensyl returns the result with warnings instead of hiding that mechanism.

stiffness.validity == result.validity means the warnings stay attached when the ABD stiffness is passed to a geometry field, serialization workflow, or downstream adapter.

Diagnostics

Homogenization results include:

• diagnostics["symmetric"];
• diagnostics["positive_semidefinite"];
• diagnostics["rank"];
• member and cell metadata where available.

Malformed or unsupported inputs raise typed homogenization exceptions. Finite rank-deficient assemblies are returned with diagnostics and warnings so the caller can decide whether the mechanism is acceptable.

Comparing ABD Stiffnesses

Compare ABD stiffnesses block by block:

• compare A, B, D, and As;
• compare coupling ratios and warnings;
• rotate stiffnesses into a common frame before comparing anisotropic blocks;
• avoid comparing scalar equivalent moduli unless the reduction assumptions are stated.