Skin and Laminate ABD Stiffness

This example starts with the smallest useful ABD stiffness, then replaces the isotropic skin with a symmetric laminate.

All examples in this section use one consistent US customary unit set unless noted otherwise: length in in, force in lbf, and stress in psi. Tensyl does not convert units; it only carries unit labels when you export data. The unit policy lives in Units and Consistency.

Isotropic Skin

Build a skin-only ABD stiffness for a flat reference surface. Because the reference surface is the skin mid-surface, the membrane-bending coupling block B should be zero.

from tensyl import IsotropicMaterial, isotropic_plate

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

assert stiffness.A.shape == (3, 3)
assert stiffness.B.shape == (3, 3)
assert stiffness.D.shape == (3, 3)
assert stiffness.As.shape == (2, 2)
assert abs(stiffness.B).max() == 0.0

Interpretation

This verifies the ABD block shapes and the expected zero coupling for a symmetric isotropic skin. It does not include stiffeners, shell curvature, local failure, or buckling — one thing at a time.

Symmetric Laminate

Now replace the isotropic skin with a small symmetric cross-ply laminate. The workflow is still skin-only, but stiffness depends on ply material, thickness, and angle.

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
assert stiffness.A[0, 0] > stiffness.A[1, 1]

The A block is not isotropic anymore. 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.