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!

Plot of the deflected structure, Wireframe mode

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).