MSR/ressources/Equivalent Single Layer Theories.md

To [[Composite laminate models|model a composite laminate]] there are a few options, the most important are the equivalent single layer and the [[Layerwise Theories|layerwise]].

Those theories works by computing the homogenized material properties, and solving only at the mid plane. 
The laminate is therefore modeled as an equivalent single anisotropic layer. They are useful for global response for thin laminates and are computationnally inexpensive.
-> most popular : FSDT

*They have issue with layers of different properties.*

#### Classical Laminate Theory (CLT) :
Hypothesis : The normal line to the median plane of the plate before deformation stays normal to the plane after deformation.
-> lack of transverse shear
(see [[Kirchhoff's hypothesis]])

(extension of the **Kirchhoff-Love** plate theory)

#### First-order Shear Deformation Theory (FSDT) :
Hypothesis : The normal line to the median plane of the plate stays straight after deformation but it is not normal to the middle plane, the shear constraint stays constant along the thickness of the plate.

Only two assumptions remains :
- *straight lines normal to the mid-surface remain straight after deformation*
- *the thickness of the plate does not change during a deformation.*

#### High-order Shear Deformation theory (HSDT) :
More complex variation of the shear constraint along the thickness of the plate, but more computationally expensive.

 It is assumed that the displacements are of higher order polynomial form and are $C^1$ continuous through the thickness. This allows for non-linear variation of displacements, strain and stresses through the thickness.
([[Secondary articles descriptions#First order Zig-Zag plate Theory|source]])