5

5.2 CRANE TRUSS WITH TRUSSES NO.4

Copy the example file B2_X.DXF to Z88X.DXF.

B2_X.DXF ---> Z88X.DXF input file for CAD converter Z88X

CAD:

In this example you should only look at the CAD FE 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 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 Z88I1.TXT, Z88I2.TXT and Z88I3.TXT. Windows: Compute > Z88X > Type Conversion > 5 from Z88X.DXF to Z88I*.TXT (the default) > Compute > Go, UNIX: pushbutton DXF <-> Z88 with radiobutton DXF -> I* (Z88-Commander) or z88x -iafx ("i all from dxf") (console or X-term).

Z88P, look at finite element structure. First delete the file Z88P.STO. Then Z88P loads the structure file Z88I1.TXT per default. Windows: Plot > Z88P, UNIX: with the Z88-Commander pushbutton Plot feature and radiobutton Z88P or enter from an X-term z88p. Now try Z88O.

Z88F, calculates deflections. You can 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).

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

Z88P, look at the deflected finite element structure. The deflections are magnified per default by the factor 100 which is correct for this example. Windows: Plot > Z88P > Structure > Deflected UNIX: Z88-Commander: pushbutton Plot feature and radiobutton Z88P or enter from an X-term z88p, click radiobutton Deflected. Showing von Mises stresses is not provided for Trusses No.4, because only normal stresses do exist. But with the new Z88O you may plot the tensile stresses as „von Mises stresses". Have a try!

The example is simple and straight. Experiment with the 3Ds possibilities of the plot program Z88P and the new OpenGL plot program Z88O.

A crane truss consists of 54 trusses, 20 nodes and forms a spatial framework. The nodes 1, 2 and 19, 20 are fixed, the nodes 7 and 8 are loaded per -30,000 N. The total length is 12 m . The inputs in the sample file are in mm but inputs in meters are just as possible if the other entries like Young's modulus and cross-sectional area also refer to meters (or yards or inches). The Young's modulus is 200,000 N/mm*mm, Poisson's ratio 0.3, the cross-sectional area 500 mm**2 each.

This example is taken from the (very good) book SCHWARZ, H.R.: FORTRAN Programme zur Methode der Finiten Elemente. Teubner Verlag, Stuttgart, Germany 1984.

Take into account: The header file Z88I3.TXT for the stress processor can have any content for Trusses No.4. For mixed frameworks containing hexahedrons and trusses, the entries in Z88I3.TXT do only apply for the hexahedrons.

5.2.1 Input

With CAD program:

Proceed after the description chapter 2.7.2. Do not forget to write on the layer Z88EIO the element descriptions by TEXT function:

FE 1 4 (1st finite element type 4)

FE 2 4 (2nd finite element type 4)

..........(Information not shown for elements 3 to 53)

FE 54 4 (54th finite element type 4)

Write on the layer Z88GEN the general information and material information, like

Z88I1.TXT 3 20 54 60 1 0 0 0 (3-D,20 nodes,54 ele,60 DOF, 1 mat info, flags 0 )

MAT 1 1 54 200000 0.3 1 500 (1st mat info from element 1 to element 54,Young's modulus, Poisson's ratio, INTORD (any), QPARA is cross-section area of the trusses)

Since Trusses No.4 are structure elements (and thus cannot be subdivided like finite elements), the mesh generator cannot be used. You can immediately write the boundary conditions with the TEXT function on the layer Z88RBD: The structure should be fixed to the node 1, 2 and 19, 20. A load of 30,000 N each is applied to the nodes 7 and 8. The load should be applied downward, therefore -30,000 N.

Z88I2.TXT 10 (10 boundary conditions altogether)

RBD 1 1 2 2 0 (1st BC: Node 1, DOF 2, Displacement 0 (=fixed in Y direction)

RBD 2 1 3 2 0 (2nd BC: Node 1, DOF 3, Displacement 0 (=fixed in Z direction)

RBD 3 2 1 2 0 (3rd BC: Node 2, DOF 1, Displacement 0 (=fixed in X direction)

RBD 4 2 3 2 0 (4th BC: Node 2, DOF 3, Displacement 0 (=fixed in Z direction)

RBD 5 7 3 1 -30000 (5th BC: Node 7, DOF 3, load -30,000)

RBD 6 8 3 1 -30000

RBD 7 19 1 2 0

RBD 8 19 3 2 0

RBD 9 20 2 2 0

RBD 10 20 3 2 0

... And write on the layer Z88GEN into any free place of your drawing the stress parameters for the stress calculation:

Z88I3.TXT 0 0 0 (any stress parameters for Trusses No.4)

Export the drawing as DXF file with the name Z88X.DXF and then launch the CAD converter Z88X with the option "from Z88X.DXF to Z88I*.TXT" (DXF -> I*). The CAD converter will produce the input files Z88I1.TXT, Z88I2.TXT, Z88I3.TXT.

With an editor:

Enter the structure data into Z88I1.TXT by editor (cf. section 3.2):

3 20 54 60 1 0 0 0 (3-dim,20 nodes,54 elements,60 DOF, 1 mat info line,flags 0)

1 3 0 2000 0 (1st node, 3 DOF, X, Y and Z coordinate)

2 3 0 0 0 (2nd node, 3 DOF, X, Y und Z coordinate)

3 3 1000 1000 2000

4 3 2000 2000 0

5 3 2000 0 0

........... (nodes 6 ..18 dropped here)

19 3 12000 2000 0

20 3 12000 0 0

1 4 (1st element, type Truss No.4)

1 2 (coincidence 1st element)

2 4 (2nd element, type Truss No.4)

4 5 (coincidence 2nd element)

3 4

7 8

.......... (elements 4 ..53 dropped here)

54 4

17 19

1 54 200000 0.3 1 500 (mat info from ele 1 to 54,Young's modulus,Poisson's ratio, INTORD (any), QPARA is cross-section area of the trusses)

The structure should be fixed to the node 1, 2 and 19, 20. A load of 30,000 N each is applied to the nodes 7 and 8. The load should be applied downward, therefore -30,000 N. Ref. to 3.4:

10 (10 boundary conditions)

1 2 2 0 (1st BC: Node 1, DOF 2, Displacement 0 (=fixed in Y direction)

1 3 2 0 (2nd BC: Node 1, DOF 3, Displacement 0 (=fixed in Z direction)

2 1 2 0 (3rd BC: Node 2, DOF 1, Displacement 0 (=fixed in X direction)

2 3 2 0 (4th BC: Node 2, DOF 3, Displacement 0 (=fixed in Z direction)

7 3 1 -30000 (5th BC: Node 7, DOF 3, load -30,000)

8 3 1 -30000

19 1 2 0

19 3 2 0

20 2 2 0

20 3 2 0

The parameter file for the stress processor Z88I3.TXT can have any content (cf. sections 3.5 and 4.4), because Gauss points, radial and tangential stresses as well as calculation of the von Mises stresses have no significance for Trusses No.4.

CAD and editor:

Because now the structure data Z88I1.TXT, the boundary conditions Z88I2.TXT and the header file for the stress processor Z88I3.TXT (with any content) do exist, you can launch

>Z88F Cholesky solver for computing the deflections

>Z88D stress processor

>Z88E nodal force processor

5.2.2 Results

The Cholesky solver Z88F provides the following output files:

Z88O0.TXT stores the processed structure data. It is meant for documentation purposes mainly.

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 do not depend on the header parameters in Z88I3.TXT for Trusses No.4.

The nodal force processor Z88E uses internally 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 = 100 each (magnifications of the deflections):

You can rotate the structure of this 3D example under Windows with the buttons F2.. F7 or > Zoom > Rotation X- etc. or UNIX with the Pushbuttons RX+, RX-,... RZ- around the three spatial axises in steps of 10 degrees each. F8 (Windows) or Rot 0 (UNIX) resets the rotations to zero.

Do zooming under Windows with the keys PRIOR or NEXT or with > Zoom > More or > Zoom > Less. And under UNIX with the Pushbuttons Zoom+ or Zoom- .

Do panning under Windows with the cursor keys LEFT, RIGHT, UP, DOWN and HOME or END, under UNIX with the Pushbuttons X+, X-, ... Z-.

In addition, you should try out the different views provided by Z88P: Windows: > View > XY, XZ, YZ, 3-Dim or UNIX: Radio box XY, XZ, YZ, 3D.

Von Mises stresses are not provided in the plot program for Trusses No.4. But new Z88O does it. Why don’t you try it?