4.20
PLATE NO.20 WITH 8 NODES
This is a curvilinear
Serendipity Reissner- Mindlin plate element with square shape
functions.
The transformation is isoparametric. The integration is carried out
numerically
in both axises according to Gauss- Legendre. Consequently, the
integration
order can be selected in Z88I1.TXT in the material information lines.
The order
2 (= 2 x 2 points) is mostly sufficient (reduced integration). This
element
calculates both displacements and stresses quite good. The integration
order
can be chosen again for the stress calculation. The stresses are
calculated in
the corner nodes (good for an overview) or calculated in the Gauss
points
(substantially more exactly). Area loads are defined in the appropriate
material lines, file Z88I1.TXT, instead
of Second moment of inertia RIYY. For
this element you need to set the plate flag IPFLAG to 1. Attention: In
contrary
to the usual rules of the classic mechanics Z88 defines ThetaX the
rotation
around the X- axis and ThetaY the rotation around the Y- axis.
This element type is
implemented for use with automeshers e.g. Pro/MECHANICA for
the 3D CAD system Pro/ENGINEER by
Parametric Technology. In addition, a mesh generation with Z88N is possible. Super elements
of type 20 cannot only generate finite elements of type 20, but plates
of type
19, too.
Input:
CAD :
1-5-2-6-3-7-4-8-1, ref. chap. 2.7.2
Z88I1.TXT
> KFLAG for cartesian (0) or
cylindrical coordinates (1)
> set plate flag IPFLAG to 1 (or 2, if you want to reduce the shear
influence)
> set surface and pressure loads flag IQFLAG to 0 for your
convenience. Then
the entry of the pressure is done via the "Second moment of inertia
RIYY", see below. If IQFLAG is set to 1, then the entry of the pressure
is
done via the surface and pressure loads file Z88I5.TXT
> 3 degrees of freedom for each
node (w, ThetaX, ThetaY )
> Element type is 20
> 8 nodes per element
> Cross-section parameter QPARA is the element thickness
> "Second moment of inertia RIYY" is the area load
> Integration order INTORD per each mat info line. 2 is usually
good.
Z88I3.TXT
> Integration order INTORD: Basically, it is a good idea to
use the
same value as chosen in Z88I1.TXT , but different values are permitted
0 = Calculation of the stresses in the corner nodes
1, 2, 3, 4 = Calculation of the stresses in the Gauss points
> KFLAG has no meaning
> Reduced stress flag
ISFLAG:
0 = no calculation of reduced
stresses
1 = von Mises stresses in the Gauss points ( INTORD not 0 !)
2 = principal stresses in the Gauss points (INTORD not 0!)
3 = Tresca stresses in the Gauss
points (INTORD not 0!)
This file is optional and normally
not used here because it is much more convenient to enter the pressure
data for
the plate elements into Z88I1.TXT in the
section
material information. However, the possibility for entering the
pressure loads
by the surface and pressure loads file Z88I5.TXT, too, is implemented
for
universal use of this file. Then set IQFLAG to 1 and proceed as follows:
>
Element number with pressure load
>
Pressure, positive if poiting towards the
edge
Results:
Displacements in Z (i.e. w) and rotations ThetaX
around X- axis and ThetaY around the Y- axis.
Stresses: The stresses are calculated in the corner nodes or
Gauss
points and printed along with their locations. The following results
will be
presented:
- plate
bending moments Mxx and Myy (unit: force x lenght
/ length)
- plate
torsion moments Mxy = Myx (unit: force x length /
length)
- the shear
forces Qyz and Qzx (unit: force / length)
- the true
stresses resulting from plate bending moments and plate torsion moments
Optional von Mises
stresses
Nodal forces in X and Y for each element and each node.