jd marked bug 5271 as a duplicate of bug 9157 on 1/25/19.
Both bugs arrived at the same conclusion regarding invariability of stress in-plane being the expected result of the
bi-linear shape functions of these low order formulations [assuming uniform thickness].

ELFORMs 2 and 16 are uniform thickness shells and so will use the average of the 4 thickness values given in *element_shell_thickness.               
ELFORMs 1 and 6 retain unique nodal thicknesses, i.e. these shells can act as tapered shells, so even though the strains don't vary 
amongst the in-plane integration points (Gauss points), the stresses will vary according to the thickness.

jd
2/15/19
_____________________________________________________________________

The following discussion is within the context of explicit analysis.

The formulations from left to right in the graph on p. 64 of the 971 Users Manual are:

2
2 with BWC=1 in *control_shell
8
10
11
1
16
7
6

A somewhat subjective ranking of quad shell formulations, considering both speed and robustness, is

1. type 2
2. type 2 with BWC warping stiffness and full projection (see BWC and PROJ in *control_shell)
3. type 10
4. type 16  
5. type 7
6. type 6 [1]

'Robustness' is meant here as an ability to remain stable under 
adverse conditions such as poor element shapes and 
large deformation/distortion.  Choices 2 and 3 above are, as you might expect, 
close to a tie in terms of performance 
and speed.  The last 3 formulations listed above are fully-integrated (4 in-plane integration points) 
and thus do not suffer from hourglass modes[2].
Generally speaking, the underintegrated elements 
tend to be a little too soft.  By using stiffness-based 
hourglass control (HG type 4) and a reduced hourglass 
coefficient (say, .03 to .05), the behavior is stiffened slightly 
and so this hourglass combination is generally recommended for 
most applications of the underintegrated shells.  
For very high velocity/rate problems, viscosity-based hourglass control is recommended.

From an accuracy standpoint, shell type 16 is preferred over the underintegrated 
formulations provided the following are true:

- initial element shape is reasonable
- element does not distort unreasonably during the simulation

_________________________
Recommendation from a highly respected source hinges on element size:
  element characteristic length < 4 mm  : go [ELFORM] 16
  element characteristic length > 8 mm  : go [ELFORM] 2

  between 4 and 8 mm make your own decision

  of course this assumes your aspect ratios are good, meaning
  inferior to 2

  it is based on a number of convergence studies that I have
  done or had access to in the last 20 years and is certainly
  limited to folding problems of thin ( t about 1 mm ) sheets like
  in automotive bodies
Paul Du Bois  5/7/2011
_________________________

For large in-plane shearing deformation, form 1 (Jaumann stress update) is better 
than form 2 (corotational stress update) and may also be better than form 16.
To include warping stiffness in form 1, set IRNXX=-2 in *control_shell.

______________________
Notes:

1. Formulation 6 with IRNXX set to -2 in *control_shell, while expensive, has been observed to give accurate 
springback response subsequent to a transient simulation involving large rotations, e.g., spinning blade.  
Also, this formulation is able to represent a 
tapered (nonuniform) thickness in the element.

2. ELFORMS 6 and 7 are subject to a single, warping mode of hourglassing, owing to the S/R (selective reduced) 
integration employed to prevent transverse shear locking.  In this S/R integration, 
full integration (4 in-plane integration points) is employed for 4 of the 6 stresses while 
a single integration point is used for the transverse shear stresses. 

ELFORM Formulation 16 uses a Bathe-Dvorkin transverse shear treatment which eliminates 
the w-mode, or warping mode, hourglassing.
For certain composite materials,
laminate shell theory can be invoked by setting LAMSHT=1 in *control_shell.  
This option removes the usual assumption of uniform shear strain through the 
thickness of the shell -- this is important for sandwich composites with soft
cores.

Type 16 shells require approximately 2.5 times more CPU than type 2 shells.
Used together with hourglass control type 8, the type 16 shell will give
the correct solution for warped geometries.

____________ Some type 16 shell bug history ______________

r85890 2013-12-06 
Hopefully final fix of shell 16, hourglass 8 and irnxx=-2

r85609  2013-11-23 
change to type 16 shell to eliminate instability observed with
irnxx=-2 and hourglass control type 8

_____________________________________________________________________
Miscellaneous:

NFAIL1 and NFAIL4 in control_shell can be invoked to automatically delete
highly distorted shells (negative jacobians) before they lead to an overall instability. 

When ESORT=1, all triangular shells which are not assigned a triangular element 
formulation by the user, e.g., ELFORM 3, will automatically take on 
the C0 formulation (ELFORM 4).   
Triangular shells assigned ELFORM 16 will automatically become ELFORM 4 regardless of the value of ESORT. 

It is generally recommended that invarient node numbering be invoked by setting INN=2 or 4 in 
*control_accuracy.  This is especially important when the material is orthotropic.


REFERENCES to 2006 Theory Manual:
Section 7 in the 2006 Edition of the Theory Manual addresses formulation 2.

Shell formulation 16 is discussed in Section 9 of the Theory Manual. 

Section 10 addresses formulation 1 with Section 10.6 extending the
discussion to formulations 6 and 7.

Laminate shell theory (LAMSHT in *control_shell) is discussed in Section 11
of the Theory Manual.


See ftp://ftp.lstc.com/outgoing/support/FAQ_docs/compare_element_formulations.pdf for comparisons of
ELASTIC solutions using several shell and solid element formulations to analytic solutions.
Sensitivity to mesh density is examined.


Triangular formulation 17 is NOT recommended for thick 3-noded shells (Dilip, 6/10/11).

jpd