Terminology

ABD Stiffness

An ABD stiffness is the local rule that turns plate or shell deformation into force and moment resultants. Given membrane strain, curvature, and transverse shear measured on a reference surface, it answers: what membrane forces, bending moments, and shear resultants does this wall produce?

That rule only has meaning in a stated local frame \(\{\mathbf e_1,\mathbf e_2,\mathbf n\}\). The same numeric stiffness can describe a flat panel, a cylindrical barrel, a dome, or another shell midsurface, but only after the local directions and reference surface are clear. The ABD stiffness owns the local mechanics; the surface owns the geometry and shell kinematics.

Tensyl uses the word "stiffness" deliberately. This object is not the whole plate, shell, laminate, or solver model. It is the constitutive law those models can consume. The first concrete class is ABDStiffness, which stores one canonical \(8 \times 8\) linear tangent with read-only block views A, B, D, and As.

Concept Model

Tensyl object	Engineering object	What it represents
IsotropicMaterial, OrthotropicPlyMaterial	material property set	Constituent stiffness and density values before any section thickness or stacking operation.
Ply, isotropic_plate, laminate_plate	skin or laminate	A plate/shell skin ABD stiffness about a reference surface.
BeamSection	stiffener section stiffness values	Centroidal member stiffness products such as EA, EIy, EIz, GJ, and shear stiffnesses.
BeamMember, StiffenerFamily	stiffener member or repeated family	A straight member contribution with angle, length or spacing, eccentricity, and multiplicity.
CanonicalUnitCell	repeating stiffened panel cell	The tangent-plane area represented by one repeated stiffener pattern.
HomogenizationResult	equivalent-stiffness computation result	The computed ABD stiffness plus diagnostics, assumptions, source, and validity report.
StiffnessField	spatial distribution of ABD stiffnesses	A rule for obtaining an ABD stiffness at a point on a surface.
Surface	shell midsurface geometry	Positions, local frames, metric, curvature, and radius data for embedding ABD stiffnesses.

Name Mapping

Tensyl name	Structural-engineering name
ABDStiffness	equivalent ABD stiffness or shell stiffness model
A	extensional or membrane stiffness block
B	membrane-bending coupling stiffness block
D	bending and twisting stiffness block
As	transverse-shear stiffness block
BeamSection	stiffener section stiffness values
CanonicalUnitCell	repeating stiffened panel cell
StiffnessField	spatial distribution of ABD stiffnesses over a surface
ValidityReport	scale-separation and coupling warning report

ABD Blocks

Block	Engineering meaning	Common US units	Common SI units
A	membrane stiffness	lbf/in	N/m
B	membrane-bending coupling	lbf	N
D	bending and twisting stiffness	lbf*in	N*m
As	transverse-shear stiffness	lbf/in	N/m

B is zero for many symmetric skins about their mid-surface. Eccentric stiffeners, unsymmetric laminates, or an intentionally shifted reference surface commonly make B nonzero.

Resultants

Membrane resultants N11, N22, and N12 are force per unit length. Bending resultants M11, M22, and M12 are moment per unit length. Transverse-shear resultants Q13 and Q23 are force per unit length.

Why Not Scalar Equivalent Modulus?

A scalar equivalent modulus is a derived interpretation, not the primary Tensyl output. Scalar reductions can hide anisotropy, membrane-bending coupling, twist coupling, transverse-shear behavior, and frame orientation. Tensyl keeps the full ABD and transverse-shear operator as the primary result. Use scalar engineering constants only when the reduction assumptions are stated and the stiffness is sufficiently close to the reduced model.

Stiffener Pitch and Cell Area

Pitch is the spacing between repeated stiffeners or repeated cells. A cell area is the tangent-plane area represented by one canonical repeating unit.

Equivalent-stiffness homogenization is most defensible when pitch is small compared with the response length scale that the model is meant to capture.

Eccentricity

Stiffener eccentricity is the signed distance from the reference surface to the stiffener centroid along the positive surface normal. Eccentricity drives membrane-bending coupling in the equivalent ABD stiffness.

Tangent Plane

Tangent-plane homogenization treats the repeating cell as locally flat. Surface curvature enters later through shell kinematics and validity checks, not through the first local cell stiffness assembly.