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Laminate Composites > Laminates theory > First order shear deformation theory

Off-axis relationships

The in-plane strains in the 12 coordinate system are related to the same quantities expressed in the XY coordinate system.

The transverse strains in the 12 coordinate system are related to the same quantities expressed in the XY coordinate system.

This relationship also allows the transformation of the transverse shear stresses.

The inverse of this relationship is written

The in-plane stresses in the 12 coordinate system are related to the same quantities expressed in the XY coordinate system.

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First order shear deformation theory

Strain displacement relationship

Constitutive equations

Shell stress resultants

Laminate stiffness matrices

Transverse shear stiffness matrix

Shear deformation theory references

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Off-axis relationships, Simcenter 3D 2021.1 Series

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Source: https://docs.sw.siemens.com/en-US/doc/289054037/PL20200601120302950.advanced/id626786 · retrieved 2026-07-17