Fiber Orientation May Be Inconsistent with WindIO

[JustinPorter88]

The fiber orientation in SONATA may be inconsistent with the WindIO definition. The WindIO definition (https://windio.readthedocs.io/en/latest/source/blade.html#internal-structure-2d-fem) states:

'Looking from blade root, positive angles represent a rotation of the fibers towards the leading edge of the blade.'

On the other hand, example 0_beams uses simply 30 degrees to represent the beam from the paper (see that folder) with fibers going opposite directions on the top and bottom surfaces of the beam, see (does not exactly use WindIO format):

SONATA/examples/0_beams/0_box_beam_HT_antisym_layup_15_6_SI_SmithChopra91.yaml

Lines 54 to 74 in 50b6794

	- [0., 1., 0.127, 30, 1, 'wall']
	- [0., 1., 0.127, 0, 1, 'wall']
	- [0., 1., 0.127, 30, 1, 'wall']
	- [0., 1., 0.127, 0, 1, 'wall']
	- [0., 1., 0.127, 30, 1, 'wall']
	- [0., 1., 0.127, 0, 1, 'wall']
	# --- r/R = 1.0 ---
	- position: 1.0
	trim_mass: False
	mesh_resolution: 100 # ca 450 punkte auf der aeusseren Kurve. - von innen nach aussen.
	segments:
	- id: 0
	filler: Null
	layup:
	#-[Start[-], End[-], thickness[m], Orientation [deg], MatID[int], 'name'[str]]
	- [0., 1., 0.127, 30, 1, 'wall']
	- [0., 1., 0.127, 0, 1, 'wall']
	- [0., 1., 0.127, 30, 1, 'wall']
	- [0., 1., 0.127, 0, 1, 'wall']
	- [0., 1., 0.127, 30, 1, 'wall']
	- [0., 1., 0.127, 0, 1, 'wall']

I currently suspect that the fiber orientation is around an outward or inward layer normal at each element. This would allow for a more natural definition for layers that wrap around the leading/trailing edge.

This issue also appears to happen when running through the WindIO format. See this example:
https://github.com/WISDEM/SONATA/blob/develop/examples/8_fiber_orient/8_sonata_orientation.py
The local stresses in the three elements (material coordinates) match. However, the global stresses have different signs on sigma13 and sigma12 on the top versus bottom of the beam. Part of the difference is that theta_1 (layer orientation) is different from the top to the bottom. One would need to look closer at the stress-strain relations to fully verify the orientation of the fiber_orientation of the layers.
In this example, all cells see the same 15 degree fiber rotation angle, so the WindIO wrapper for SONATA is not flipping the fiber orientation on any layers.

Current Recommendations

1. Manually verify stress-strain relations using SONATA to recover stresses and strains in global coordinates to verify that the rotation of the layer is in the desired direction.
2. If suspicions above are confirmed, then the fiber orientation on one of the suction or pressure side would need to be flipped in the input yaml file. I have not yet confirmed which one needs to be flipped from the WindIO definition.

[JustinPorter88]

Commit c18a2c2 simplified the example. Shows that global strains flip in the 2 direction while local strains stay the same when flipping the cell definition between these two options:

cells = np.array([[3, 0, 1, 2]])
cells = np.array([[1, 2, 3, 0]])

This is equivalent to flipping between the suction and pressure (or pressure and suction) side of the mesh. If the fiber_orientation always pointed to leading edge, this should not change either the global or local strains. Still have not confirmed which of suction or pressure side matches WindIO definition.