First order shear deformation theory

Laminate Composites is based on the First-order Shear Deformation Theory, FSDT [1] [2]. This theory is similar to Classical Lamination Theory (CLT) [3] [4] [1] [5]. Notable differences between the two are:

• CLT assumes no transverse shear deformation, whereas in FSDT a constant shear deformation and force are predicted through the thickness of the laminate.

• FSDT requires continuity of the transverse displacement and in-plane rotational degrees of freedom (so-called Co continuity). On the other hand, CLT requires continuity of the transverse displacement and of its first derivative with respect to both in-plane coordinates (so-called C1 continuity).

For these reasons, FSDT lends itself well to finite element discretization.

Notation

The XY plane is located at the reference plane of the laminate. The XY–axes correspond to the material orientation coordinate system, which is also called the laminate coordinate system. Each ply is numbered consecutively starting with the bottom ply. Plies are located by their Z coordinate with respect to the reference plane: Ply k is located between coordinates Zk-1 and Zk. The figure below shows the definition of the 12 ply coordinate system corresponding to ply N. The angle θk measures the angle between the X and 1 axes. Because angles are positive according to the right-hand rule convention, angle θN has a positive numerical value whereas θ3 is negative.

Assumptions

1. Upon deformation, sections perpendicular to the reference plane remain plane.

2. Each ply is in a state of plane stress.

3. Plies are perfectly bonded.

4. Strains and displacements are small.

Look up more details

Strain displacement relationship

Constitutive equations

Off-axis relationships

Shell stress resultants

Laminate stiffness matrices

Transverse shear stiffness matrix

Shear deformation theory references

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First order shear deformation theory, Simcenter 3D 2021.1 Series

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