In order to measure the distortion of the quadrilateral face of a solid element, a
unique reference plane is defined by two auxiliary plane vectors.
The plane vectors are calculated as:
PL
1
=
(
V
3
+
V
2
)
−
(
V
1
+
V
4
)
PL
2
=
(
V
3
+
V
4
)
−
(
V
1
+
V
2
)
where,
V
1
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf
MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi
ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8
qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9
q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake
aacaWGwbWaaSbaaSqaaiaaigdaaeqaaaaa@3A99@
,
V
2
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf
MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi
ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8
qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9
q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake
aacaWGwbWaaSbaaSqaaiaaigdaaeqaaaaa@3A99@
,
V
3
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf
MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi
ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8
qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9
q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake
aacaWGwbWaaSbaaSqaaiaaigdaaeqaaaaa@3A99@
, and
V
4
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf
MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi
ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8
qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9
q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake
aacaWGwbWaaSbaaSqaaiaaigdaaeqaaaaa@3A99@
are the vectors that connect the four corner nodes
with the centroid of the quadrilateral. These two plane vectors and the centroid are
then used to construct the reference plane.
Figure 1 . Vectors of a Non-warping Quadrilateral Face