NONLINEAR STATIC AND DYNAMIC STRUCTURAL ANALYSIS

7/29/2019 NONLINEAR STATIC AND DYNAMIC STRUCTURAL ANALYSIS

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Faculty of Mechanical Engineering of Kragujevac

Laboratory for Engineering Software

Miroslav ivkovi Sneana Vulovi

NNOONNLLIINNEEAARRSSTTAATTIICC AANNDD DDYYNNAAMMIICCSSTTRRUUCCTTUURRAALL AANNAALLYYSSIISS

PPRREE-- AANNDD PPOOSSTT-- PPRROOCCEESSSSIINNGG EEXXAAMMPPLLEESS IINN PPRROOGGRRAAMM FFEEMMAAPPFFOORRPPRROOGGRRAAMM PPAACCKKAAGGEE PPAAKKK

Kragujevac

SERBIA


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Faculty of Mechanical Engineering

ENGINEERING SOFTWARE LAB

Sestre Janjic 6, 34000 Kragujevac, SERBIA

Tel: +381 34 300790

Fax: +381 34 300791

Mob: +381 64 8288777

e-mail: [email protected]


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CONTENTS

EXAMPLE 1. Elasto-plastic analysis of rods ..................................................1

EXAMPLE 2. Elasto-plastic analysis of rods .................................................27

3

EXAMPLE 3. Elasto-plastic analysis of rods .................................................53

L

EXAMPLE 4. (SG_9) Large displacement with snap-through behavior ......79

X

Y

1

2

3

A12=0.02

A23=1

EXAMPLE 5. (SG_10) Post-critical snap-back analysis ..............................99

EXAMPLE 6. (SG_4) Large displacements of circle arc ............................119

EXAMPLE 7. (SG_6) Large displacements of a simple beam with localbuckling ................................................................................143

EXAMPLE 8. Snap-through and snap-back of a shell ................................169


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z

x

yC

F

B

A

F

EXAMPLE 9. Shrinkage of a cylinder with free edges ...............................201

EXAMPLE 10 - Half of sphere with hole subjected to concentrated forces 227

EXAMPLE 11. Deflection of a square test tube during uniaxial tension

(Yoshida-test) .......................................................................255

EXAMPLE 12. (SG_12) Large strain necking of circular bar .....................289

EXAMPLE 13. (SG_13) Large strain necking of rectangular bar ...............323


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PAK-S Examples Nonlinear Structural Analysis

Example 1 1

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EXAMPLE 1. Elasto-plastic analysis of rods

Description/Objective At first, we shell observe a simple example, where only the effects ofmaterial non-linearity should be taken into consideration (Fig. 1). We shell assume that

displacements and deformations are small and that loads are applied slowly (statically), i.e. that

inertial forces are to be neglected. The force variation is presented in Fig. 1. Determine the

dependence between displacements, stress and force F.

Fig. 1

Suggested Exercise Steps:

I. Defining Materials and Properties

II. Generation of Nodes and Elements

III. Constraining the Model

IV. Loading the Model

V. Prepare and Submit the Model for a Nonlinear Analysis

VI. Postprocessing and Review the Results

E=2E8 kN/m2

=0T=2.4E5 kN/m

2

E T=2E7 kN/m2

A1=10 cm2

A2=8 cm

2

l1=0.5m

l2=1 m

Force[kN]

Time [s]


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Example 1 2

If you have not already done so, start FEMAP by double-click the icon on your Desktop or in the

Windows Start menu, pickStart>Programs>Femap v8.1>Femap v8.1. All new models are named

Untitled. The command File>Save As... allows you to change the model filename. The WindowsCommon File Save As dialog box will be display. Using this box, you can navigate around your

local computer. Move to or create a directory where you wish to store your FEMAP model, type in

the field File name Example1, and press Save.Throughout this example, all commands that you will select from the FEMAP menu will be shown

in the following styleFile>Save As...Which means, first select File from the menu, and then moveto the Save Ascommand.

File>Save As...

Tools>Advanced Geometry...

I_1. Defining Materials and Properties

Rods are made of elastic-plastic material.

Model>Material...

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Example 1 3

AfterFEMAP displays dialog boxDefine Isotropic Material - Nonlinear pressOK, than againdisplays dialog boxDefine Isotropic MaterialpressCancel.

Remark: In a message window at the bottom of the screen, you can see a confirmation that material

is created.

Model>Property...

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Example 1 4

Create the second property.

AfterFEMAP displays again dialog boxDefine Property - ROD Element TypepressCancel.

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Example 1 5

II_1. Generation of Nodes and Elements

Model>Node (Ctrl+N)

The next dialogue box appears, in which the coordinates of the first node are entered.

Repeat the procedure for other nodes.

AfterFEMAP displays again dialog boxLocate Enter Coordinates or Select with Cursorpress Cancel.

Press Ctrl+A or choose following command to autoscale the view:

View>Autoscale>Visible

Display labelling of nodes and elements by ID

View>Options... (F6)

The following dialogue box appears

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Example 1 6

Model>Element... (Ctrl+E)


Select the nodes or enter the number of nodes. However, it is easier to use graphical interface and to

select nodes at the screen by using the mouse. Click on the first Nodes box and select the nodes atthe screen in order shown in previous dialogue.

Remark: A node nearest to the cursor will be highlighted by yellow X( ), by mouse click,highlighted node will be selected - you do not need to precisely click on a node!

Repeat the procedure for the second element.

After FEMAP displays again dialog box Define ROD Element - Enter Nodes or Select with

CursorpressCancel.

You can turn off the workplane for the clarity of model picture.

Tools>Workplane... (F2)

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Example 1 7

You can change the colors of model entities (nodes) using next commands:

Modify>Color>Node...

Modify>Color>Elements...

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Example 1 8

Use the following command to regenerate the screen:

View>Regenerate (Ctrl+G)

On the Fig.2 finite element model (nodes and elements) is shown.

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Example 1 9

III_1. Constraining the Model

Note: Since Constraints are Set based, you must create an empty Constrain Set before defining anyactual constrains.

Model>Constraint>Set... (Shift+F2)

Model>Constraint>Nodal...

Note: Graphically (using mouse) pick the location of nodes in which constraints are given (1 and 3)on screen, Fig.2. They will be marked by +1 and +3 and added to Entity Selection box, so they

could not be selected (marked) again.

AfterFEMAP displays again dialog boxEntity Selection - Enter Node(s) to Selectpress Cancel.

Modify>Update other>Perm Constraint...

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Example 1 10

IV_1. Loading the Model

Modal>Function...

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Example 1 11

AfterFEMAP displays again dialog boxFunction Definitionpress Cancel.

Note: Since Load are Set based, you must create an empty Load Set before defining any actual load.

Modal>Load>Set... (Ctrl+F2)

Modal>Load>Nodal

Force at node 2 should be specifying.

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Example 1 12

AfterFEMAP displays again dialog box Entity Selection Enter Node(s) to Select press Cancel.

To reduce the amount of information displayed (turn off Perm Constraint), use the FEMAPQuickOptions (short-cut keyCtrl+Q):

The Fig. 3 shows a finite element model with numbering of nodes and elements and given

constraints and loads.

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Example 1 13

X

Y

Z

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1

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1.

Fig. 3

Save your model by pressing F4.

V_1. Prepare and Submit the Model for a Nonlinear Analysis

You should export your model as FEMAP neutral file (*.NEU file ver.4.4). Then, using the PAK

Translator you will translate your model into an input file for FEA program PAK-S that willanalyze this model.

File>Export>FEMAP Neutral

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Example 1 14

Run the PAK Translator by double-click the icon on your Desktop or in the directory Paktrrunthe filePaktr.exe.

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Example 1 15

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Example 1 16

Close the Pak Translator with command:

File>Exit

You should save your*. dat file in the same directory as you put a filePaks.exe. You need to run

filePaks.exe (by double-click)and after start it, typeExample1.datin a DOS prompt (see thewindow below). Three files should be create during this processExample1. LST,Example1. UNV,

Example1. NEU.

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Example 1 17

VI_1. Postprocesing and Review the Results

After solution, FEMAP can read the output results for post-processing. Reading output results is

similar like writing model for analysis.

File>Import>FEMAP Neutral

Plot force-displacement diagram at node 2.

View>Select... (F5)

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Example 1 18

For curve 2 adjust: Output Vector: APPLIED LOAD; Node: 2.

AfterFEMAP displays again dialog boxView Selectpress OK.

In order to plot dependence between two variables, they is necessary to export diagram data.

Writing diagram data into ASCII data file.

List>Destination...

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Example 1 19

File Example1pp.lst is now opened.

Writing diagram data in previously opened file with command:

List>Output>XY Plot...

Diagram data will be written in file Example1pp.lst.

Transfer of file data to Excel

Open the file in which diagram data are written (Example1pp.lst) in a text editor (UltraEdit,

Notepad and similar). Contents of Example1pp.lst file are shown in the following Fig. 4.

Fig. 4

Displacements and forces are diametrical to y-axis direction, so, it is necessary to change their signs

for the table values.

Start the EXCEL by clicking on icon at the desktop or by clicking on

Start>Programs> Microsoft Office>Microsoft Office Excel

In this example, we want to show connection between displacements and rod force.

By using the clipboard, we shall transfer data from file Example1pp.lst to Excel.

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Example 1 20

Select displacements in node 2, values under Y for all time steps (turn on column selection in

UltraEdit using Alt+C). Press Ctrl+C or Edit/Copy (to copy select data in the clipboard).

By using Alt+Tab transfer to Excel and with Ctrl+V or Edit/Paste copy the clipboard contents to the

first column, starting from the second row of the Excel sheet.

The same procedure should be applied for copying the force values in node 2 in the clipboard.

With Alt+Tab transfer to Excel and with Ctrl+V or Edit/Paste copy the clipboard contents to the

second column, starting from the second row of the Excel sheet. Add zero values for displacementand force at the first row of the first and the second column. The Excel table appearance is shown

in the Fig. 5.

Fig. 5

Plotting the diagrams

By clicking on icon for plotting the charts (Chart ), Excel's wizard for plotting the charts isactuated. Chart plotting is conducted in 4 steps.

The first step: Choose the type and subtype of the chart which you want to plot. Choose the type

and subtype as shown in the following dialogue.

The second step: define the chart data. Click on a Series tab;

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Example 1 21

The first curve: by clicking on Add button, text boxes for entering curve data are opened.Name: Force-displacement

X Values: Click on button at the end of the text box, previous dialogue box will shrink. Select

all values of the first column; the references of the marked table fields will appear in

dialogue box and they will be marked with dashed lines (see window below)

By another click on icon, dialogue box spreads again.

Y Values: click on button at the end of the text box and then select all values from the second

column.

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Example 1 22

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Example 1 23

The third step: adjustment of chart options.

Titles tab: Chart title: the chart title can be entered in previous step and will be written above the

diagram

Value (X) axis: name for values plotted on X-axis (displacements)

Value (Y) axis: name for values plotted on Y-axis (force)

Axes tab: By checking Value (X/Y) axis, values will be shown on x/y axes.

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Example 1 24

Gridlines tab: adjustment of parameters for drawing the grids on chart.

Legend tab: By checking Show legend, a legend will be shown at the chart, it is necessary to selectwhere it will be shown.

Data labels tab: turning on/turning off the values on chart. By selecting Show value, y-values are

shown at chart; by selecting show label, x-values are shown at chart.

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Example 1 25

The fourth step: selecting the chart location; on a new sheet (by selecting as new sheet, a new sheetwill be created in a file named Chart) or as an object in sheet (As object in) selected from the dropdown menu.

By clicking on Finish button, a following chart appears.

Force-dispalcement

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0 0,0005 0,001 0,0015 0,002 0,0025 0,003 0,0035 0,004

Displacement

Force

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Example 1 26


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Example 2 27


Description/Objective A structure composed of 7 perfectly plastic rods is analyzed by LNDRmethod (Arc length + Newton-Raphson method). Geometry changes are considered. A model is

shown in the following figure. Determine the dependences between displacements and force.

Fig. 1









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Example 2 28







File>Save As...




Model>Material...

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Example 2 29

AfterFEMAP displays dialog boxDefine Isotropic Material - NonlinearpressOK.


is created.

Repeat the procedure for the second material.

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Example 2 30

AfterFEMAP displays dialog boxDefine Isotropic Material - Nonlinear pressOK, then againdisplays dialog boxDefine Isotropic MaterialpressCancel.

Model>Property...

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Example 2 31

Repeat the procedure for the second property.


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Example 2 32


Model>Node... (Ctrl+N)






Display labeling of nodes and elements by ID



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Example 2 33




select nodes at the screen by using the mouse. Click on the first Nodes box and select the nodes at

the screen in order shown in previous dialogue.Remark: A node nearest to the cursor will be highlighted by yellow X( ), by mouse click,highlighted node will be selected - you do not need to precisely click on a node!

Repeat the procedure for other elements.

2 3

1

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2

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Example 2 34

After FEMAP displays again dialog box Define ROD Element - Enter Nodes or Select withCursorpressCancel.





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Example 2 35





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Example 2 36

X

Y

Z

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4 5

6 7

1

2 3

4

5

Fig. 2


Note: Since Constraints are set based, you must create an empty Constrain Set before defining any

actual constrains.Model>Constraint>Set... (Shift+F2)


Note: Graphically pick the location of nodes in which constraints are given (1 and 4) on screen,Fig.2. They will be marked by +1 and +4 and added toEntity Selection box, so they could not be

selected (marked) again.

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Example 2 37






Modal>Load>Nodal...

Force at nodes 2 and 3 should be specified.

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Example 2 38


To reduce the amount of information displayed (turn off Perm Constraint), use the FEMAP Quick

Options (short-cut keyCtrl+Q):

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Example 2 39



X

Y

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2 3

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12 12

1. 1.

Fig. 3



You should export your model as FEMAP neutral file (*.NEU file ver.4.4). Then, using the PAKTranslator you will translate your model into an input file for FEA program PAK-S that willanalyze this model.



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Example 2 40


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Example 2 41

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Example 2 42

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Data for automatic load stepping:

Node number: Node with controlled displacement.

Direction: Controlled degree of freedom of node.

Value: Value of controlled displacement.

AG: Coefficient of increase of displacement

DS: Coefficient of arc lenght increase.


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Example 2 43


File>Exit.


filePaks.exeand after start it, typeExample2.datin a DOS prompt (see the window below). Threefiles should be creating during this processExample2. LST,Example2. UNV,Example2. NEU.

VI_2. Postprocesing and Review the ResultsAfter solution, FEMAP can read the output results for post-processing. Reading output results is



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Example 2 44


View>Select... (F5)

For curve 2 adjust: Output Vector: CRITICAL LOAD; Node: 2.

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Example 2 45


In order to plot dependence between two variables, they is necessary to export diagram data.


List>Destination...

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Example 2 46







Notepad and similar).











second column, starting from the second row of the Excel sheet. Add zero values for displacement

and force at the first row of the first and the second column. The Excel table appearance is shown

in the Fig. 4.

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Example 2 47

Fig. 4






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Example 2 48




dialogue box and they will be marked with dashed lines.


Y Values: click on button at the end of the text box and then select all values from the secondcolumn.

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Example 2 49

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Example 2 50



diagram


Value (Y) axis: name for values plotted on Y-axis (force).


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Example 2 51





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Example 2 52



Force-displacement

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Displacement

Force

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Example 3 53


Description/Objective A structure composed of 3 perfectly plastic rods, which geometry changesare taken into account, was analyzed by LNDR method (Arc length + Newton-Raphson method). A

model is shown in Fig. 1. Determine the dependence between displacements and force P.

3

Fig. 1









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Example 3 54



Untitled. The commandFile>Save As...allows you to change the model filename. The WindowsCommon File Save As dialog box will be display. Using this box, you can navigate around your



in the following styleFile>Save As...Which means, first selectFile from the menu, and then moveto the Save Ascommand.

File>Save As...




Model>Material...

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Example 3 55

AfterFEMAP displays dialog boxDefine Isotropic Material - NonlinearpressOK.


is created.

Repeat the procedure for the second material.

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Example 3 56

AfterFEMAP displays dialog boxDefine Isotropic Material - Nonlinear pressOK, then againdisplays dialog boxDefine Isotropic MaterialpressCancel.

Model>Property...

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Example 3 57

Repeat the procedure for the second property.


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Example 3 58


Model>Node... (Ctrl+N)









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Example 3 59





the screen in order shown in previous dialogue.


Repeat the procedure for other elements.




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Example 3 60




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Example 3 61




X

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Fig. 2




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Example 3 62


Note: Graphically pick the location of nodes in which constraints are given (1, 2 and 4) on screen,Fig.2. They will be marked by +1, +2 and +4 and added to Entity Selectionbox, so they could not

be selected (marked) again.



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Example 3 63


Note: Since Load are Set based, you must create an empty Load Set before defining any actual load.Modal>Load>Set... (Ctrl+F2)

Modal>Load>Nodal...





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Example 3 64

The Fig. 3 shows a finite element model with numbering of nodes and elements and givenconstraints and loads.

X

Y

Z

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Fig. 3


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Example 3 65





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Example 3 66

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Example 3 67

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Example 3 68


File>Exit.


filePaks.exeand after start it, typeExample3.datin a DOS prompt (see the window below). Threefiles should be create during this processExample3. LST,Example3. UNV,Example3. NEU.

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Example 3 69






View>Select... (F5)

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Example 3 70



In order to plot dependence between two variables, it is necessary to export diagram data. Writing

diagram data into ASCII data file.

List>Destination...

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Example 3 71



List>Output>XY Plot




Notepad and similar).













in the Fig. 4.

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Example 3 72

Fig. 4






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Example 3 73






Y Values: click on button at the end of the text box and then select all values from the second

column.

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Example 3 74

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Example 3 75



diagram




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Example 3 76





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Example 3 77



Force-displacement

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500

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Displacment

Force

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Example 3 78


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Example 4 79

EXAMPLE 4. (SG_9) Large displacement with snap-throughbehavior

Description/Objective We shell observe a simple example, a rod with a force directed in oppositedirection (Fig. 1). This example illustrates the procedures for automatic selection of loads in the

area of sub-critical behavior. Incremental procedures with monotonic increase in levels of outerloads can not comprise a complete behavior of such structure. Analytical connection between force,

F, and displacement is analogue to expression:

( )YLYLYLL

EAFo

++=

00

2000sin

sin2

11

where Y is displacement of the point at which the force is given.

L

Fig. 1

The example is solved with constant arc length method and the solution agrees with analytical

solution.








E=2.1E6

=0.3A=1

L=10


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Example 4 80







File>Save As...



Model>Material...

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Example 4 81


is created.AfterFEMAP displays dialog boxDefine Isotropic MaterialpressCancel.

Model>Property...

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Example 4 82



Model>Node... (Ctrl+N)The next dialogue box appears, in which the coordinates of the first node are entered.

Repeat the procedure for the second node.

AfterFEMAPdisplays again dialog boxLocate Enter Coordinates or Select with Cursorpress Cancel.





The following dialogue box appears.

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Example 4 83












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Example 4 84




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Example 4 85


X

Y

Z

1

1

2

Fig. 2





Note: Graphically (using mouse) pick the location of nodes in which constraints are given (1) onscreen, Fig.2. It will be marked by +1 and added toEntity Selectionbox, so it could not be selected

(marked) again.

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2

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Example 4 86

Now, select node 2.

AfterFEMAPdisplays again dialog boxEntity Selection - Enter Node(s) to Selectpress Cancel.





Modal>Load>Nodal...


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Example 4 87




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Example 4 88



X

Y

Z

1

1

2

12

1

1.

Fig. 3


V_4. Prepare and Submit the Model for a Nonlinear AnalysisYou should export your model as FEMAP neutral file (*.NEU file ver.4.4). Then, using the PAKTranslator you will translate your model into an input file for FEA program PAK-S that willanalyze this model.


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Example 4 89


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Example 4 90

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Example 4 91


File>Exit.


filePaks.exeand after start it, typeExample4.datin a DOS prompt (see the window below). Threefiles should be create during this processExample4. LST,Example4. UNV,Example4. NEU.

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Example 4 92






View>Select... (F5)

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Example 4 93



In order to plot dependence between two variables, it is necessary to export diagram data. Writing

diagram data into ASCII data file.

List>Destination...

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Example 4 94







Notepad and similar). Displacements are diametrical to y-axis direction, so, it is necessary to

change those signs of the values in table.







By using Alt+Tab transfer to Excel and with Ctrl+V or Edit/Paste copy the clipboard contents to thefirst column, starting from the second row of the Excel sheet.





in the Fig. 4.

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2 3

1


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Example 4 95

Fig. 4



The first step: Choose the type and subtype of the chart you want to plot. Choose the type and

subtype as shown in the following dialogue. Press buttonNext to pass on the next step.


The firs curve: by clicking on Add button, text boxes for entering curve data are opened.Name: Force-displacement






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Example 4 96

Y Values: click on button at the end of the text box and then select all values from the third

column.

Press buttonNext to pass on the next step.



diagram.

Value (X) axis: name for values plotted on X-axis (displacements).




Legend tab: By checking Show legend, a legend will be shown at the chart, it is necessary to select

where it will be shown.Data labels tab: turning on/turning off the values on chart. By selecting Show value, y-values are



The fourth step: selecting the chart location; on a new sheet (by selecting As new sheet, a newsheet will be created in a file named Chart) or as an object in sheet (As object in) selected from thedrop down menu.

By clicking on Finish button, the following chart appears.


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Example 4 97

Force-displacement

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0

5000

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15000

0 1 2 3 4 5 6 7

Displacement

Force

Fig. 5


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Example 4 98


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Example 6 99

EXAMPLE 5. (SG_10) Post-critical snap-back analysis

Description/Objective Based on previous example, then following model is formulated, in whichan effect known as "snap-back" occurs. According to Fig. 1, it is obvious that the dependence force

F - displacement Y is the same as in previous example.

X

Y

1

2

3

A12=0.02

A23

=1

Fig. 1

In border conditions, when a rod 12 is absolutely stiff, displacement X is for every value of force F

equal to displacement Y. In real conditions, displacements X and Y are equal only in the case when

F=0. Solution is obtained by the use of LDNR method, with displacement of node 1 (U*=0.1)

being given at the first step, and the total number of steps being 40.






V. Prepare and Submit the Model for a Nonlinear AnalysisVI. Postprocessing and Review the Results

E=2.1E6

=0.3L=10


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Example 6 100







File>Save As...



Model>Material...

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Example 6 101


is created.AfterFEMAP displays dialog boxDefine Isotropic MaterialpressCancel.

Model>Property...

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Example 6 102

Generation of the second property.


II_5. Generation of Nodes and ElementsModel>Node... (Ctrl+N)



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Example 6 103

AfterFEMAPdisplays again dialog boxLocate Enter Coordinates or Select with Cursorpress Cancel.












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Example 6 104







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Example 6 105




X

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Fig. 2

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Example 6 106





Note: Graphically (using mouse) pick the location of nodes in which constraints are given (3) onscreen, Fig.2. It will be marked by +3 and added toEntity Selectionbox, so it could not be selected

(marked) again.

Now, select nodes 1 and 2.


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2

1

32

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32


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Example 6 107



Note: Since Load are Set based, you must create an empty Load Set before defining any actual load.Modal>Load>Set... (Ctrl+F2)

Modal>Load>Nodal...


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Example 6 108






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Example 6 109

X

Y

Z

1

2

1

2

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1

1

12

1.

Fig. 3





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32


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Example 6 110


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Example 6 111

12

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Example 6 112

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Example 6 113


File>Exit.


filePaks.exeand after start it, typeExample5.datin a DOS prompt (see the window below). Three

files should be create during this processExample5. LST,Example5. UNV,Example5. NEU.

VI_5. Postprocesing and Review the ResultsAfter solution, FEMAP can read the output results for post-processing. Reading output results is



1

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Example 6 114

Plot force-displacement diagram at nodes 1 and 2.

View>Select... (F5)

Adjust the parameters for curve 2: Output Vector: T2 Translation; Node: 2.

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2

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Example 6 115



In order to plot dependence between two variables, it is necessary to export diagram data.


List>Destination...

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14

2

1


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Example 6 116







Notepad and similar). Displacements are diametrical to y-axis direction, so, it is necessary to

change signs of the values in table.





Select displacements in node 1, values under Y for all time steps (turn on column selection in Ultra

Edit using Alt+C). Press Ctrl+C or Edit/Copy (to copy select data in the clipboard).


first column, starting from the second row of the Excel sheet.The same procedure should be applied for copying the displacements in node 2 and force values in

node 1 to Excel.

Displacements in node 2 copy to the second column, starting from the second row of Excel sheet

and force values to the third column, starting from the second row of the Excel sheet. Add zero

values for displacements and force at the first row of the first, the second and the third column.

1

2 3

1


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Example 6 117



The first step: Choose the type and subtype of the chart you want to plot. Choose the type and

subtype as shown in the following dialogue. Press buttonNext to pass on the next step.


The first curve: by clicking on Add button, text boxes for entering curve data are opened.Name: X-displacement

X Values: Click on button at the end of the

text box, previous dialogue box will

shrink. Select all values of the first

column; the references of themarked table fields will appear in

dialogue box and they will be

marked with dashed lines.

By another click on icon, dialogue box

spreads again.

Y Values: click on button at the end of the

text box and then select all values

from the third column.

The second curve: by clicking on Add button,text boxes for entering the second curve data are

openedName: Y-displacement

X-values: click on a button at the end of the

text box and previous dialog box

will shrink. Select all values from

the second column.

By another click on icon, dialogue box spreads again

Y-values: click on button at the end of the text box and then select all values from the third

column.


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Example 6 118




diagram.

Value (X) axis: name for values plotted on X-axis (displacements).




Legend tab: By checking Show legend, a legend will be shown at the chart, it is necessary to select

where it will be shown (check top).




The fourth step: selecting the chart location; on a new sheet (by selecting As new sheet, a new sheetwill be created in a file named Chart) or as an object in sheet (As object in) selected from the dropdown menu.

By clicking on Finish button, the following chart appears.

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

0 1 2 3 4 5 6 7

Displacement

Force

X displacement Y displacement

Fig. 5


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Example 6 119

EXAMPLE 6. (SG_4) Large displacements of circle arc

Description/Objective Circle arc having unsymmetrical supports is loaded by force (Fig. 1). Forceincrease causes large displacements of a structure. Material is isotropic and elastic. Example shows

the application of iterative arc-length method, follows the history of deformation of the structure

with snap-through and snap-back effects.

Fig. 1



II. Creating the Geometry

III. Generation of Nodes and Elements

IV. Constraining the Model

V. Loading the Model

VI. Prepare and Submit the Model for a Nonlinear Analysis

VII. Postprocessing and Review the Results


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Example 6 120







File>Save As...



Model>Material...

AfterFEMAP displays dialog boxDefine Isotropic MaterialpressCancel.

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1

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Example 6 121

Model>Property...

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Example 6 122

AfterFEMAP displays again dialog boxDefine Property - MEMBRANE Element Type pressCancel.

II_6. Creating the Geometry

We shall create circle arc on an active workplane by entering the coordinates of a center, beginning

and final points of arc.

Geometry>Curve-Arc>Center-Start-End...

Created circle arc is plotted at the screen, let's create another circle arc.

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Example 6 123

AfterFEMAP displays again dialog box Locate Enter Location at Center of ArcpressCancel.

Adjustment of a view of whole drawing at the screen with command:

View>Autoscale>Visible (Ctrl+A)



Use the short-cut key Ctrl+G to regenerate the screen.

A following figure is now shown at the screen, Fig. 2.

Fig. 2

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Example 6 124

Let's define a surface between created arcs.

Geometry>Surface>Ruled...

AfterFEMAP displays again dialog box Create Ruled Surfacepress Cancel.A surface shown in the following figure (Fig. 3) will be created from selected arcs and straight lines(created by joining corresponding ends of arcs).

Fig. 3

III_6. Generation of Nodes and Elements

Note: The first thing which we need to do is to set the mesh size for surface.

Mesh>Mesh Control>Mapped Divisions on Surface...

Note: You can graphically pick the location of surface on screen, Fig.3.

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2

1

3


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Example 6 125

AfterFEMAP displays again dialog box Entity Selection - Select Surface(s) to Set Mesh Sizepress Cancel.Now we will create nodes and elements on the surface.

Mesh>Geometry>Surface...

To reduce the amount of information displayed (turn off geometry), use the FEMAP Quick Options

(short-cut keyCtrl+Q):

Display labelling of nodes by ID


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Example 6 126

Finite element model is shown in the Fig 4.

X

Y

Z

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14151617

1819

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45464748

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Fig. 4

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Example 6 127

IV_6. Constraining the Model




Note: Graphically (using mouse) pick the location of nodes in which constraints are given (31, 62and 32) on screen, Fig.4.



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2

1

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Example 6 128

V_6. Loading the Model



Modal>Load>Nodal...





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Example 6 129

The Fig. 5 shows a finite element model with numbering of nodes and elements and givenconstraints and load.

X

Y

Z

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1.

Fig. 5


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Example 6 130

VI_6. Prepare and Submit the Model for a Nonlinear Analysis




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Documents

NONLINEAR STATIC AND DYNAMIC STRUCTURAL ANALYSIS