5

5.1 FORK WRENCH WITH PLANE STRESS ELE. NO.7

Copy the example files B1_* into Z88 entry files Z88* (has been already carried out on the Z88 diskettes for your immediate start):

B1_X.DXF ---> Z88X.DXF input file for CAD converter Z88X

B1_2.TXT ---> Z88I2.TXT boundary conditions for Cholesky solver Z88F

B1_3.TXT ---> Z88I3.TXT header parameters for stress processor Z88D

Simply proceed with the following steps to get familiar with Z88:

CAD:

As for this first example, you should only look at the CAD super structure without producing it. This comes with later examples. Import Z88X.DXF into your CAD program and view it. Usually you would draw or model the super structure in your CAD system. Do not change anything and leave your CAD program without saving, converting etc. If you do not have any suitable CAD system, then drop this step.

Z88:

Z88X, conversion from Z88X.DXF to Z88NI.TXT. Windows: Compute > Z88X > Type Conversion > 6 from Z88X.DXF to Z88NI.TXT > Compute > Go, UNIX: pushbutton DXF <-> Z88 with radiobutton DXF -> NI (Z88-Commander) or z88x -nifx (console or X-term).

Z88P, looking at the super structure. The error message should not disturb you, because Z88P still has no .STO file and therefore expects Z88I1.TXT to load (which is not yet present). However, you want to load Z88NI.TXT: Windows: Plot > Z88P > File > Structure File > Z88NI.TXT, UNIX: with the Z88-Commander pushbutton Plot feature and radiobutton Z88P or enter from an X-term z88p, enter z88ni.txt in textfield Struc., press Return. Now try Z88O.

Z88N, mesh generator, reads Z88NI.TXT and produces Z88I1.TXT. Windows: Compute > Z88N > Compute > Go. UNIX: pushbutton Z88N (Z88-Commander) or z88n (console or X-term).

Z88P, look at the finite element structure. Z88P now has a Z88P.STO file from the former Run and expects Z88NI.TXT to load. Now you want to load Z88I1.TXT. Windows: Plot > Z88P > File > Structure File > Z88I1.TXT, UNIX:, with the Z88-Commander pushbutton Plot feature and radiobutton Z88P or enter from an X-term z88p, enter z88i1.txt in textfield Struc., press Return. This could have been avoided if you would have deleted the file Z88P.STO before start of Z88P, because Z88P.STO stores all parameters of the last Z88P run. If Z88P.STO does not exist, Z88P works with default values, for example Z88I1.TXT as structure file.

Z88F, calculates displacements. Use the Compactmode: Windows: Compute > Z88F > Mode > Compactmode, > Compute > Go, UNIX: pushbutton Z88F with radiobutton Compact M (Z88-Commander) or z88f -c (console or X-term).

Z88D, calculates stresses. Windows: Compute > Z88D > Compute > Go, UNIX: pushbutton Z88D (Z88-Commander) or z88d (console or X-term).

Z88P, look at the deflected finite element structure. Z88P has a .STO file and thus features correct parameters. The displacements are multiplied per default by the factor 100, which is a bit too large for this example. Windows: Plot > Z88P > Factors > Deflections > enter 10 for FUX and FUY each, > Structure > Deflected UNIX: Z88-Commander: pushbutton Plot feature and radiobutton Z88P or enter from an X-term z88p, enter 10 into both textfields FUX and FUY, press either a Return for each textfield or pushbutton Regen. Click radiobutton Deflected. Because Z88D has been already run, you can display the von Mises stresses right now. Go to Undeflected structure. Windows: > Mises Stresses > Show von Mises stresses. UNIX: Togglebutton Mises . Furthermore you could produce a plotter file, perhaps undeflected and without von Mises stresses. Windows: > Output > Plotter. UNIX: Pushbutton Plot. The resulting plot file Z88O6.TXT contains HP-GL commands.

Z88E, nodal forces calculation. Windows: Compute > Z88E > Compute > Go, UNIX: pushbutton Z88E (Z88-Commander) or enter z88e from a console or X-term.

Your task:

A fork wrench should be loaded with the screw's tightness torque. A couple of forces are applied in the wrench's mouth according to the torque and the fixed points are assumed to be at the locations where the mechanic's hand grips the wrench. In fact, these clever boundary conditions are doing the same task as (in reality !) the fixed points in the mouth and the forces applied to the grip, but are much easier to handle.

The fork wrench should be modelled by 7 super elements Plane Stress No.7. The mesh generator should produce 66 finite elements from the super elements. The element thickness is 10 mm each. Mesh generation: Local and global axises are not the same direction in this example: Local x direction at super element 1 defines by the local nodes 1 and 2 which correspond to the global nodes 1 and 3. The local y direction of SE 1 is determined by local nodes 1 and 4 which correspond to the global nodes 1 and 7. Further take into account: Super elements which have a joint side must have an absolutely identical subdivision at this side. Thus, SE 1 and SE 2 share the line 3-4-5: The subdivisions in y direction must be exactly the same. Here 3 subdivisions, respectively.

Now calculate this example as indicated above. After that, one can experiment: Subdivide the SE 7 in Z88NI.TXT as a meaningful variation as follows:

7 7 ("Super element 7 is of type 7, i.e. Plane Stress Element No.7")

6 L 3 E ( "Subdivide SE 7 into finite elements Plane Stress No.7 and subdivide into x

direction 6 times geometrically ascending and in y direction 3 times equidistant")

Of course, the SE 1 to SE 5 as well could each be condensed in direction of the screw:

1 7

3 L 3 E

2 7

3 L 3 E

.... continue ....

Note: As it is obvious for the input files, you can add comments after all required data are entered in every line. Separate the last date from the comment by at least one blank. You can do this just the same in your own files. A maximum of altogether 250 characters per line is permitted.

5.1.1 Input

This example works with a super structure, i.e. a very rough FE mesh. The mesh generator should generate a FE structure from the super structure. Thus, the first task is to design the mesh generator input file Z88NI.TXT. Chapter 2.6 outlines the procedure if working with CAD. If you work without a CAD system, you design the file Z88NI.TXT by editor or word processing program. The super structure shall look as follows:

With CAD program:

Follow the description of chapter 2.7. Do not forget to write the super element information on the layer Z88EIO by TEXT function. Thus

SE 1 7 7 3 E 3 E ( 1st SE, SE type 7, FE type 7, subdivide into x 3 times equid., into y 3 times equid. )

SE 2 7 7 3 E 3 E ( 2nd SE, SE type 7, FE type 7, subdivide into X 3 times equid., into y 3 times equid. )

SE 3 7 7 3 E 3 E

SE 4 7 7 3 E 3 E

SE 5 7 7 3 E 3 E

SE 6 7 7 1 E 3 E

SE 7 7 7 6 E 3 E

...and write the general information and material information onto the layer Z88GEN :

Z88NI.TXT 2 38 7 76 1 0 0 0 0 ( 2-DIM, 38 nodes, 7 superelements, 76 DOF, 1 mat info, flags 0 )

MAT 1 1 7 206000 0.3 3 10 ( 1.mat info from SE 1 to SE 7: Young's modulus, Poisson's ratio, INTORD, thickness, )

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 Z88P.

With editor:

Write the mesh generator input file Z88NI.TXT (cf. chapter 3.3) with an editor:

2 38 7 76 1 0 0 0 0 (2-DIM, 38 nodes, 7 superelements, 76 DOF, 1 mat info line, flags 0)

1 2 22.040 32.175 (Node 1, 2 DOF, X and Y coordinates)

2 2 31.913 28.798 (Node 2, 2 DOF, X and Y coordinates)

3 2 43.781 24.826

4 2 43.880 32.373

5 2 43.980 39.424

...... (Coordinates for nodes 6... 36 not represented)

37 2 202.847 27.507

38 2 144.905 42.403

1 7 (SE 1 of the type Plane Stress No.7)

1 3 5 7 2 4 6 8 (Coincidence for 1st SE)

2 7 (SE 2 of the type Plane Stress No. 7)

3 10 12 5 9 11 13 4 (Coincidence for 2nd SE)

..... (Coincidence for elements 3 .. 6 droped here)

7 7

30 35 37 32 34 36 38 31

1 7 206000 0.3 3 10 (mat info from SE 1 to SE 7:Young,Poisson,INTORD,thickness)

1 7 (Subdivide 1st SE into FE type 7 and

3 E 3 E subdivide into x 3 times equidistant + into y 3 times equidistant)

2 7 (Subdivide 2nd SE into FE type 7 and

3 E 3 E subdivide into x 3 times equidistant + into y 3 times equidistant)

3 7

3 E 3 E

4 7

3 E 3 E

5 7

3 E 3 E

6 7

1 E 3 E

7 7

6 E 3 E

With CAD program and editor:

Start the mesh generator Z88N for producing the final Z88 structure file Z88I1.TXT. Look at it either

- in the CAD program (from Z88I1.TXT to Z88X.DXF, I1 -> DXF) after conversion with Z88X or
- with the Z88 plot program Z88P for defining the boundary conditions:

Enlarge the wrench's mouth by zooming for defining the two nodes which will get the load representing the torque (to simplify matters it is assumed, that the screw gets only selectively a couple of forces as torque at the corners and that the screw itself and not the wrench revolves):

We find the nodes 11 and 143. The pictures printed here were produced directly by Z88P.

In the same way both the nodes for fixing the wrench are determined and the boundary conditions are entered in the plot program or CAD system:

In the CAD program:

Switch to the layer Z88RBD and write with the TEXT function into any free place:

Z88I2.TXT 16 (16 Boundary conditions altogether)

RBD 1 11 2 1 -7143 (1st BC: Node 11, DOF 2, Force -7,143 N assumed)

RBD 2 143 2 1 7143 (2nd BC: Node 143, DOF 2, Force 7,143 N assumed)

RBD 3 216 1 2 0 (3rd BC: Node 216, DOF 1, Displacement 0 (= fixed) assumed)

RBD 4 216 2 2 0

RBD 5 220 1 2 0

RBD 6 220 2 2 0

RBD 7 227 1 2 0

RBD 8 227 2 2 0

RBD 9 231 1 2 0

RBD 10 231 2 2 0

RBD 11 238 1 2 0

RBD 12 238 2 2 0

RBD 13 242 1 2 0

RBD 14 242 2 2 0

RBD 15 249 1 2 0

RBD 16 249 2 2 0

with an Editor:

Design the boundary condition file Z88I2.TXT by editing:

16 (16 Boundary conditions altogether)

11 2 1 -7143 (1st BC: Node 11, DOF 2, Force -7,143 N assumed)

143 2 1 7143 (2nd BC: Node 143, DOF 2, Force 7,143 N assumed)

216 1 2 0 (3rd BC: Node 216, DOF 1, Displacement 0 (= fixed) assumed)

216 2 2 0

220 1 2 0

220 2 2 0

227 1 2 0

227 2 2 0

231 1 2 0

231 2 2 0

238 1 2 0

238 2 2 0

242 1 2 0

242 2 2 0

249 1 2 0

249 2 2 0

Input for stress calculation:

In the CAD program:

Switch to the layer Z88GEN and write with the TEXT function into any free place:

Z88I3.TXT 3 0 1 ( 3x3 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 an editor:

Enter in the parameter file for the stress processor Z88I3.TXT (cf. Chapter 3.5):

3 0 1 ( 3x3 Gauss points for stresses, KFLAG 0, von Mises stresses)

Now launch the Cholesky solver Z88F and then the stress processor Z88D. You should choose for Z88F the flag -c (Compactmode) because only one set of boundary conditions is available cf. section 2.1. Basically, z88f -c (Compactmode) is always correct. You will see during the run of Z88F, that 14.848 memory places (8 bytes each) are needed in the total stiffness matrix GS. NKOI, i.e. memory places in the coincidence vector KOI, is printed as 540 (4 Bytes each). Well, this also matches Z88.DYN. Where does the number 540 come from? 66 finite elements of the type Plane Stress No.7 with 8 nodes each, makes 66*8 = 528. The number 540 results because Z88F always calculates 20 nodes for security reasons for the last finite element. Thus, NKOI becomes here: 65*8 + 20 = 540.

You calculate the nodal forces with Z88E.

5.1.2 Results

The Cholesky solver Z88F provides the following output files:

Z88O0.TXT stores the processed structure data. It is mainly intended for documentation purposes, but also shows if your input file Z88NI.TXT for the mesh generator did what you meant it to do.

Z88O1.TXT stores the processed boundary conditions: For documentation purposes. And: Was your boundary conditions input in Z88I2.TXT correctly interpreted ?

Z88O2.TXT, the displacements, the main task and solution of the FEA problem.

The stress processor Z88D uses internally 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 following picture of the plot program shows the deflected structure for FUX and FUY = 10 each (magnifications of the deflections):

The nodal force processor Z88E uses internally the calculated deflections of Z88F and stores

Z88O4.TXT, the computed nodal forces.

Z88P plots the von Mises stresses zoomed around the area of the element 12, which features the biggest von Mises stresses as pointed below. The letter J corresponds to a von Mises stress from 647 to 718 N/mm**2. Now do the same with Z88O but keep in mind that the maximum stresses are somewhat lower, ref. Chp. 2.11.