====== COQJ4 ======
Quadrangular shallow shell element

===== Description =====
  * Bending: Kirchhoff's theory in plane stress state
  * Corotational total Lagrangian formulation taking into account the curvature of the element during deformation (Marguerre theory is used in cartesian coordinates; the element converges towards a deep shell solution).
  * Plastic part computed using Green deformations (+ Piola-Kirchhoff stress) and elastic part computed with real deformation (+ Cauchy stress) ⇒ the elastic part must be negligible compared to the plastic part.
  * 4 nodes with 6 DoF each: 3 translations and 3 rotations
  * 2*2 Gauss integration points
  * Contact or uniform loading can be taken into account
Type: 45 \\
Imported from FINELG by Li Kaiping in 1991

{{  :elements:coqj4.png?500  |}}
==== Files ====
Prepro: COQJ4A.F \\
Lagamine: COQJ4B.F

===== Input file =====
^Title (A5)^^
|TITLE|"COQJ4" in the first 5 columns|
^Control data (3I5)^^
|NELEM|Number of elements|
|ILOC|Index for actualization of local axes \\ = 0 → New approach (Recommanded default value) \\ = 1 → Old approach (problem with step size)|
|INDPP| = 0 → No specific density (Static analysis: NTANA > 0) \\ = 1 → Specific density taken into account (Dynamic analysis: NTANA < 0)|
^Density - only if INDPP = 1 (dynamic analysis only) (2G10.0)^^
|WSPE(4)|Density|
|DMASS_ROT|Multiplicative factor for masses in rotation (default value =1)|
^Definition of the shell elements (2I5, G10.0)^^
|LMATE|Material law|
|NELMC|Number of elements of contact/loading associated with the shell element (0 ≤ NELMC ≤ 5)|
|THICK|Initial thickness of the shell|
^Definition of the contact/load elements (4I5) - NELMC times^^
|NPI|Number of integration points for contact/loading (4 or 9)|
|IMAT|Material law for contact/loading|
|IFUND|Number of the foundation to contact \\ > 0 there will be contact on the upper surface of the shell \\ < 0 there will be contact on the lower surface of the shell|
|IRIGF|Type of contact (same meaning as [[elements:cfi3d|CFI3D]]): \\ = 0 → foundation or rigid tool (by default) \\ = 1 → uncoupled structure/structure contact \\ = 2 → coupled structure/structure contact \\ = 3 → coupled structure/structure contact \\ = 4 → coupled structure/structure contact - pilot node|
^List of nodes of the shell element (8I5)^^
|NODES(I) \\ I=1,4|Corner nodes|
|NODESM(I) \\ I=1,4|[OPTIONAL] Nodes of the middle of the sides (A to D), used only to define the initial geometry of the element. **These nodes must be fixed along the 6 DoF**. If they are not given, they are computed automatically and placed at the middle of each side.|
==== Remark ====
It is not possible to take into account the specific weight in static analysis

===== Results =====
For each integration point:
  * Stresses (see material law)
  * State variable:
    * Q(1→NVMAX): see material law
    * Q(NVMAX+1): $e_{xM}$
    * Q(NVMAX+2): $e_{yM}$
    * Q(NVMAX+3): $e_{zM}$
    * Q(NVMAX+4): $e_{xF}$
    * Q(NVMAX+5): $e_{yF}$
    * Q(NVMAX+6): $e_{zF}$
  * If there are contact elements (see law):
    * Stresses of the contact element
    * State variables of the contact elements
State variables of the additional solid element (not printable in the .out file):
  * Local coordinates
  * Rotation matrix to change to the local frame