5.5
PLATE SEGMENT WITH HEXAHEDRONS NO.1
Copy the example files B5_*
into Z88 entry files Z88* :
B5_X.DXF ---> Z88X.DXF input file for CAD converter Z88X
B5_2.TXT ---> Z88I2.TXT boundary conditions for Cholesky solver Z88F
B5_3.TXT ---> Z88I3.TXT header parameters for stress processor Z88D
CAD:
Import Z88X.DXF
into your CAD program and look at it. Usually you would have designed
this
example in a CAD system and then exported it as Z88X.DXF.
Z88: (in reduced form, more detailed
instructions cf. examples 5.1, 5.2 and 5.3 )
Z88X, conversion, "from Z88X.DXF to
Z88NI.TXT"
Z88O, looking at super structure, super
structure file Z88NI.TXT
Z88N, computes the finite element mesh
Z88O, looking at finite element
structure, structure file Z88I1.TXT, undeflected
Z88X, conversion, "from Z88I*.TXT
to Z88X.DXF"
CAD:
Import Z88X.DXF
into your CAD program and look at it. Usually you would have now added
the
boundary conditions and header parameters for Z88I3.TXT and then
exported as
Z88X.DXF.
Z88: (in reduced form, more detailed instructions
cf. examples 5.1, 5.2 and 5.3)
Z88X, conversion, "from Z88X.DXF to
Z88I*.TXT"
Z88F calculates deflections
Z88D calculates stresses
Z88O, plot FE structure, now also
deflected (FUX, FUY, FUZ per 10.), show v. Mises stresses
Z88E calculates nodal forces
We deal with a 90 degrees
disk segment which looks like a piece of tart. It is fixed at the outer
edge
and is loaded with 7,000 N at the inner edge. For such structures data
entry is
best by cylindrical coordinates. To fix the geometry two super elements
Hexahedrons
No.10 will do fine.
These two SE are now to be subdivided into 48 Hexahedrons No.1 for the FE mesh.
This example is very
suitable for experiments with the mesh generator . . if you do this, you have to define new
boundary conditions, if necessary: With the help of your CAD program or
the Z88-plot
program.
Concerning the stress
indication take into account that the stresses are plotted in the Gauss
points.
Gauss points lie within of a finite element, never directly on the
surface. One
gets stresses on the surface by extrapolation, e.g. bending stresses by
use of
the geometric analogy.
Super structure,consisting
of two Hexahedrons No.10 with 20 nodes each
5.5.1
Input
With
CAD program:
Use the description in chapter 2.7.2. Do
not forget to write the super element
information on the layer Z88EIO by TEXT function. Thus
SE 1 1
8 L 3 e
1 e (1st
super element, finite element type 1, subdivide into x 8 times
increasing, into
y 3 times equid., no subdivision into z)
SE 2
1
8
L 3 e
1 e
(2nd
super element, finite element type 1, subdivide into x 8 times
increasing, into
y 3 times equid., no subdivision into z)
Write the general
information and material information on the layer Z88GEN:
Z88NI.TXT 3 32 2
96 1 1 0
0
0 0 (3-Dim, 32
nodes, 2 SE, 96 DOF, 1 mat info
line, KFLAG 1, rest of flags is 0 )
MAT 1
1
2
206000 0.3 2 0 (1st
mat info: SE1 to SE2: Young's,
Poisson's, INTORD for FE, QPARA is 0 )
Export the drawing as DXF
file with the name Z88X.DXF and start the CAD converter Z88X with the
option
"from Z88X.DXF to Z88NI.TXT" (DXF -> NI). Z88X will produce the
mesh generator input file Z88NI.TXT. (You
should have a look at it with Z88O).
With
editor:
Write the mesh generator input file Z88NI.TXT (cf. chapter 3.3) with an
editor:
3 32 2 96 1 1 0 0
0 0 (3-Dim, 32
nodes, 2 SE, 96 DOF, 1 mat info
line, KFLAG 1, rest of flags is 0 )
1 3
20 0
5
(1st node, 3 DOF, R-, Phi and Z
coordinate)
2 3 80
0 5 (2nd
node, 3 DOF, R-, Phi and Z
coordinate)
3 3 80
45
5
...... (nodes 4.. 30 not represented)
31 3 80 90 2.5
32 3 20
90
2.5
1 10
(Super ele 1, type Hexah. No.10)
1 2
3
4
5
6
7 8
9 10
11
12 13
14
15 16 17 18
19 20
(coincidence for SE 1)
2 10 (Super
ele 2, type Hexah. No.10)
4 3
21 22 8
7 23 24 11 25 26 27
15 28 29
30 20
19 31
32
(coincidence for SE 2)
1 2 206000 0.3 2 0
(SE1
to SE2: Young's, Poisson's, INTORD for FE, QPARA is 0)
1 1 (Subdivide
SE1 into
Hexahedrons No.1 and subdivide into
8 L 3
E 1
E x
8 times increasing, into y 3 times
equid., no subdivision into z)
2 1 (Subdivide SE2 into Hexahedrons No.1 and
subdivide into
8 L 3 E
1 E
x 8 times increasing,
into y 3 times
equid., no subdivision into z)
CAD
and editor:
Start the mesh generator
Z88N to produce the
final Z88 structure file Z88I1.TXT. Look at
it either
* in the CAD program (from Z88I1.TXT to Z88X.DXF) after conversion with
Z88X or
* with the Z88 plot program Z88O for defining
the boundary
conditions:
View of the FE mesh
Z88I1.TXT produced by the mesh generator
Now determine in the plot
program or CAD system the nodes which are to be fixed or to be loaded
and enter
the boundary conditions:
In
the CAD program:
Switch to the layer Z88RBD and write with the TEXT function into any
free
place:
Z88I2.TXT 49 (49 boundary
conditions altogether)
RBD 1 1
3 1 -1000
(1st BC: Node 1, DOF 3 (=Z), a
load
of 1,000 N downward)
RBD 2
3 3 1 -1000
RBD 3 5 3 1 -1000
RBD 4 7 3
1 -1000
RBD 5 65
1 2
0 (5th
BC: Node 65, DOF 1 fixed)
RBD 6 65
2 2
0 (6th
BC: Node 65, DOF 2 fixed)
RBD 7 65
3 2
0 (7th
BC: Node 65, DOF 3 fixed)
.....(the nodes 66,67,68,69,70,71,72 are fixed in all 3 degrees of
freedom,
like node 65)
RBD 29 73
3 1
-1000
RBD 30 75
3 1 -1000
RBD 31 77
3 1 -1000
.... (the nodes 121,122,123,124,125 are fixed in all 3 degrees of
freedom,
like node 126)
RBD 47 126 1
2 0
RBD 48 126 2
2
0
RBD 49 126 3
2 0
With
editor:
Design the boundary conditions file Z88I2.TXT
by editing:
49 (49
boundary conditions altogether)
1 3 1 -1000 (Node
1, DOF 3 (=Z), a load of 1,000 N downward)
3 3 1 -1000
5 3 1 -1000
7 3 1 -1000
65 1
2 0 (Node
65, DOF 1 fixed)
65 2 2 0 (Node
65, DOF 2 fixed)
65 3 2 0
(Node 65, DOF 3 fixed)
.....(the nodes 66,67,68,69,70,71,72 are fixed in all 3 degrees of
freedom,
like node 65)
73 3 1
-1000
75 3 1
-1000
77 3 1
-1000
.... (the nodes 121,122,123,124,125 are fixed in all 3 degrees of
freedom,
like node 126)
126 1
2 0
126 2
2
0
126 3 2 0
Input for stress
calculation:
With
CAD program:
Switch to the layer Z88GEN and write into any free place:
Z88I3.TXT 2
0 1 (2x2 Gauss
points for stresses, KFLAG 0,
von Mises stresses)
Export the drawing as DXF
file with the name Z88X.DXF, then start the CAD converter Z88X with the
option
"from Z88X.DXF to Z88I*.TXT" (DXF -> I*). The CAD converter
produces the three Z88 input files Z88I1.TXT, Z88I2.TXT, Z88I3.TXT.
With
editor:
Enter the parameter file for the stress processor Z88I3.TXT (cf. Chapter 3.5):
2 0 1
( 2x2 Gauss points for stresses,
KFLAG 0,
von Mises stresses)
CAD
and editor:
Now launch the Cholesky
solver Z88F and then the stress processor Z88D. Compute nodal forces with Z88E.
5.5.2
Results
The Cholesky solver
Z88F provides the following output files:
Z88O0.TXT stores the processed structure
data. For documentation purposes.
Z88O1.TXT stores the processed boundary conditions: For
documentation
purposes.
Z88O2.TXT, the displacements, the main task and solution of the
FEA
problem.
The stress processor Z88D internally uses the calculated
displacements
from Z88F and stores Z88O3.TXT, the calculated stresses. The
results in
Z88O3.TXT depend on the header parameters in Z88I3.TXT.
The nodal force processor Z88E internally uses the calculated
deflections of Z88F and stores Z88O4.TXT, the computed nodal
forces.
The following picture of
the plot program shows the deflected structure for FUX, FUY and FUZ =
10 each
(magnifications of the deflections):
Plot of the deflected structure, Wireframe mode
Hint: The super structure is very easy to
design with e.g. AutoCAD. Draw the edges using arcs. The nodal points
can
easily be produced by the function > Draw > Point > Divide.
When
outlining the elements using the LINE function be sure to position the
view in
space exactly to match all nodes of a super element properly. This is a
common source for a later malfunction of the CAD converter Z88X!
Hint: In reality you won’t
compute such a structure with hexahedrons with linear shape functions
(Type No.1) but with
hexahedrons with quadratic shape functions (Type No.10). See Rieg, F.;
Hackenschmidt, R.: Finite Elemente Analyse für Ingenieure. 3.
Auflage. München
Wien. Carl Hanser: 2009 (in German language).