4.19
PLATE NO.19 WITH 16 NODES
This is a curvilinear Lagrange-
Reissner- Mindlin plate element with cubic 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 4 (=
4 x 4 points) is very good. This element calculates both displacements and
stresses very precisely. The input amount is heavy, you should use the mesher Z88N.
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.
Mesh generation with
Z88N: Use plates No.20 for super elements, resulting in finite elements of type 19 (plates
No.20 may generated by AutoCAD or Pro/ENGINEER, ref. the chapters of Z88X and
Z88G). A bit tricky, but works quite fine.
For example, some lines
from a mesh generator input file Z88NI.TXT:
.....
5 20 super element 5 of type 20
20 25 27 22 24 26 28 21
.....
5 19 generate from super element 5 (which is of type 20 is, see above)
finite elements of type 19
3 E 3 E .. and subdivide them threetimes equidistant in X-direction and
threetimes equidistant in Y- direction
Input:
CAD : 1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-1 , ref. chap. 2.7.2. Usually, you will not work in
this way. It's much more easier to build within a CAD program a super elements
mesh with 8- node plates No.20. Export this mesh as a DXF file and use Z88X to
produce a mesh generator input file Z88NI.TXT. Run the mesher Z88N and generate a finite elements mesh
with plates No.19. Plot this mesh using Z88P, read off the appropriate node numbers and
edit the boundary conditions file Z88I2.TXT.
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 19
> 16 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. 4 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 computed for 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 informations. 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:
Optional von Mises
stresses
Nodal forces in X and Y for each element and each node.