nonlinear analysis femap

Faculty of Engineering, University of Kragujevac Department for Applied Mechanics and Automatic

Control - Laboratory for Engineering Software

Miroslav ivkovi, PhD. Sneana Vulovi, PhD.

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PPRREE-- AANNDD PPOOSSTT-- PPRROOCCEESSSSIINNGG EEXXAAMMPPLLEESS IINN PPRROOGGRRAAMM FFEEMMAAPP

FFOORR PPRROOGGRRAAMM PPAACCKKAAGGEE PPAAKK

Kragujevac, 2013 SERBIA

Faculty of Engineering ENGINEERING SOFTWARE LAB

Sestre Janjic 6, 34000 Kragujevac, SERBIA Tel: +381 34 300790 Fax: +381 34 300791

Mob: +381 69 8288777 e-mail: [email protected]

Contents

EXAMPLE 1 Elasto-plastic analysis of rods



L

EXAMPLE 4 (SG_9) Large displacement with snap-through behaviour

X

Y

1

2

3

A12=0.02

A23=1

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

EXAMPLE 6 (SG_6) Large displacements of circle arc

EXAMPLE 7 (SG_6) Large displacements of a simple beam with local

buckling

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

z

x

yC

F

B

A

F

EXAMPLE 9 Shrinkage of a cylinder with free edges

EXAMPLE 10 (SE8_6) Half of sphere with hole subjected to concentrated

forces

EXAMPLE 11 (SG_12) Large strain necking of circular bar

EXAMPLE 12 (SG_13) Large strain necking of rectangular bar

PAK-S Examples Nonlinear Structural Analysis

Example 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 of material 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

=0 T=2.4E5 kN/m2 E T=2E7 kN/m2 A1=10 cm2 A2=8 cm2 l1=0.5m l2=1 m

Forc

e [k

N]

Time [s]


Example 1

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If you have not already done so, start FEMAP by double-click the icon on your Desktop or in the Windows Start menu, pick Start>Programs>Femap1>Femap. All new models are named Untitled. The command File>Save As... allows you to change the model filename. The Windows Common 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 style File>Save As... Which means, first select File from the menu, and then move to the Save As command. File>Save As...

1 Femap 11 is used

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Example 1

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I. Defining Materials and Properties Rods are made of elastic-plastic material.

Model>Material...

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Example 1

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After FEMAP displays dialog box Define Material - Isotropic press Cancel. Model>Property...

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Example 1

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Create the second property.

After FEMAP displays again dialog box Define Property - ROD Element Type press Cancel. II. 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.

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Example 1

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After FEMAP displays again dialog box Locate Enter Coordinates or Select with Cursor press 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

Model>Element... (Ctrl+E) The following dialogue box appears

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Example 1

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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 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 the second element.

After FEMAP displays again dialog box Define ROD Element - Enter Nodes or Select with Cursor press Cancel. You can change the colors of model entities (nodes) using next commands:

Modify>Color>Node...

Modify>Color>Elements...

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Example 1

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

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Example 1

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III. Constraining the Model Note: Since Constraints are Set based, you must create an empty Constrain Set before defining any actual constrains. Model>Constraint>Create/Manage Set... (short-cut key Shift+F2)

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Example 1

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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.

After FEMAP displays again dialog box Entity Selection - Enter Node(s) to Select press Cancel. Modify>Update other>Perm Constraint...

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Example 1

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IV. Loading the Model Modal>Function... Added dynamic XY plotting of functions to the Function Definition dialog box.

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Example 1

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Example 1

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After FEMAP displays again dialog box Function Definition press Cancel. Note: Since Load are Set based, you must create an empty Load Set before defining any actual load.

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Example 1

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Model>Load>Create/Manage Set... (short-cut key Ctrl+F2)

Modal>Load>Nodal Force at node 2 should be specifying.

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Example 1

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After FEMAP 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 FEMAP View Visibility Options (short-cut key Ctrl+Q):

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Example 1

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

Fig. 3

We suggested you to save your work that you have done till now, using File>Save (short-cut F4).

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Example 1

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V. Prepare and Submit the Model for a Nonlinear Analysis Create the input file and solve the model. Click on a PAK in main menu to start PAK translator. Pak translator should automatically create new DAT file and start PAK solver.

For nonlinear static analysis you need to input aditional parameters. To do this click on a button Edit Analysis Options after which a General Options dialog will apear.

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Example 1

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Now model is ready for the analysis. Run the PAK solver by click on the Analyse button.

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Example 1

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When the analysis is complete a dialog Analysis Complete is shown. Click on Load Results button closes PakTranslator and loads results in the Femap.

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Example 1

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VI Postprocessing and Review the Results Viewing the rod axial forces in the truss as follows: FEMAP can generate XY plots of results using the Charting dockable pane. There are two different entities in the Charting pane, Charts and Data Series. Any number of Chart entities may exist in the model and each Chart may display any number of selected Data Series. The Type of Data Series determines what will be displayed in the selected Chart. In addition, each Type of Data Series requires specific input to properly create the XY plot. If the Charting pane is already displayed, skip this step...

Tools>Charting (or click the Charting icon on the Panes Toolbar )

Click the Chart Manager icon ( ) in the Charting pane to create a new Chart.

The Charting dialog box will appear. This tabbed dialog box allows a number of options to be selected for the new chart. For this example, the default Chart settings are OK.

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Example 1

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Note: In a new model, the Chart Selector is set to 0..None/Create New by default. Because of this, when a new Data Series is created, a default Chart will also be created along with the Data Series. Therefore, it is not really required to use the Chart Manager unless you are creating multiple Charts.

Click the Chart Data Series Manager icon ( ) in the Charting pane to create a new Data Series.

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Example 1

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Example 1

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Example 1

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After FEMAP displays again dialog box Chart Data Series press Cancel.

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Example 1

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The FEMAP diagram is shown in the Fig. 4.

Fig. 4

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

Click the Copy Chart to Clipboard icon ( ) in the Charting pane to write data to Clipboard.

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 used Microsoft Office Excel 2010.)

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

By using the clipboard, we shall transfer data to Excel. With Ctrl+V or Edit/Paste copy the clipboard contents to 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. 5.


Example 1

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Fig. 5

Plotting the diagrams From Insert menu choose the type and subtype of the chart which you want to plot like in next picture:

After select type of chart blank chart is appeared on the window. Click right mouse button on white surface and pick Select data from menu.

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Example 1

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Define the chart data. Click on a Add button, Edit Series dialog are opened.

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Example 1

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

Select values of the second 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.

Series Y values: click on button at the end of the text box and then select values from the second column (see window below).

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Example 1

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By clicking on OK button, a following chart appears.

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Example 1

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Example 2 1

EXAMPLE 2. Elasto-plastic analysis of rods Description/Objective A structure composed of 7 perfectly plastic rods is analyzed by LNDR method (Arc length + Newton-Raphson method). Geometry changes are considered. A model is shown in the following figure. Determine the dependences between displacements and force.

2H =10. A =1. E =2.e5 ET =0 Y =100

Fig. 1

Suggested Exercise Steps:





Example 2 2


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Example 2 3


Model>Material...

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Example 2 4

Repeat the procedure for the second material.

After FEMAP displays dialog box Define Material - Isotropic press Cancel.

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Example 2 5

Model>Property...

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Example 2 6

Repeat the procedure for the second property.

After FEMAP displays again dialog box Define Property - ROD Element Type press Cancel.

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Example 2 7

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


After FEMAP displays again dialog box Locate Enter Coordinates or Select with Cursor press Cancel. Press Ctrl+A or choose following command to autoscale the view:

View>Autoscale>Visible Display labeling of nodes and elements by ID View>Options... (F6) The following dialogue box appears.

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Example 2 8



Repeat the procedure for other elements.

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Example 2 9

After FEMAP displays again dialog box Define ROD Element - Enter Nodes or Select with Cursor press Cancel.

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

Fig. 2

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Example 2 10

III. Constraining the Model Note: Since Constraints are set based, you must create an empty Constrain Set before defining any actual constrains. Model>Constraint>Create/Manage Set... (short-cut key Shift+F2)

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Example 2 11

Model>Constraint>Nodal... 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 to Entity Selection box, so they could not be selected (marked) again.

After FEMAP displays again dialog box Entity Selection - Enter Node(s) to Select press Cancel. Modify>Update Other>Perm Constraint...

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Example 2 12

IV. Loading the Model Note: Since Load are Set based, you must create an empty Load Set before defining any actual load. Model>Load>Create/Manage Set... (short-cut key Ctrl+F2)

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Example 2 13

Modal>Load>Nodal... Force at nodes 2 and 3 should be specified.

After FEMAP displays again dialog box Entity Selection Enter Node(s) to Select press Cancel. The Fig. 3 shows a finite element model with numbering of nodes and elements and given constraints and loads.

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Example 2 14

Fig. 3

We suggested you to save your work that you have done till now, using File>Save (short-cut F4). V. Prepare and Submit the Model for a Linear Static Analysis Create the input file and solve the model. Click on a PAK in main menu to start PAK translator. Pak translator should automatically create new DAT file and start PAK solver.

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Example 2 15


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 23

Fig. 5 Plotting the diagrams From Insert menu choose the type and subtype of the chart which you want to plot like in next picture:


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Example 2 24


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Example 2 25





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Example 2 26


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Example 2 27

Fig. 6


Example 2 28


Example 3

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EXAMPLE 3. Elasto-plastic analysis of rods Description/Objective A structure composed of 3 perfectly plastic rods, which geometry changes are 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.

Fig. 1






Example 3

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Example 3

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Model>Material...

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Example 3

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Remark: In a message window at the bottom of the screen, you can see a confirmation that material is created. Repeat the procedure for the second material.

After FEMAP displays dialog box Define Material - Isotropic press Cancel.

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Example 3

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Model>Property...

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Example 3

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Repeat the procedure for the second property.

After FEMAP displays again dialog box Define Property - ROD Element Type press Cancel. II. Generation of Nodes and Elements Model>Node... (Ctrl+N) The next dialogue box appears, in which the coordinates of the first node are entered.


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Example 3

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After FEMAP displays again dialog box Locate Enter Coordinates or Select with Cursor press 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 3

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Repeat the procedure for other elements.

After FEMAP displays again dialog box Define ROD Element - Enter Nodes or Select with Cursor press Cancel. On the Fig. 2 finite element model (nodes and elements) is shown.

Fig. 2

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Example 3

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Example 3

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Model>Constraint>Nodal... 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 Selection box, so they could not be selected (marked) again.


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Example 3

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Example 3

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Modal>Load>Nodal... Force at node 3 should be specifying.

After FEMAP 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 FEMAP View Visibility Options (short-cut key Ctrl+Q):

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Example 3

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Fig. 3

Save your model by pressing F4.

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Example 3

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Example 4 1

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

Description/Objective We shell observe a simple example, a rod with a force directed in opposite direction (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 outer loads can not comprise a complete behavior of such structure. Analytical connection between force, F, and displacement is analogue to expression:

YLYLYLL

EAF o

00

2000sin

sin211

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. Suggested Exercise Steps:




E=2.1E6 =0.3 A=1 L=10


Example 4 2


1 Femap 11 is used

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Example 4 3


Model>Material...

Remark: In a message window at the bottom of the screen, you can see a confirmation that material is created. After FEMAP displays dialog box Define Material - Isotropic press Cancel.

Model>Property...

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Example 4 4


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Example 4 5


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

Repeat the procedure for the second node.

After FEMAP displays again dialog box Locate Enter Coordinates or Select with Cursor press 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 4 6

Model>Element... (Ctrl+E) The following dialogue box appears.



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Example 4 7


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Example 4 8

Model>Constraint>Nodal... Note: Graphically (using mouse) pick the location of nodes in which constraints are given (1) on screen, Fig. 2. It will be marked by +1 and added to Entity Selection box, so it could not be selected (marked) again.

Now, select node 2.


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Example 5 1

EXAMPLE 5. (SG_10) Post-critical snap-back analysis Description/Objective Based on previous example, then following model is formulated, in which an 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

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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. Suggested Exercise Steps:




E=2.1E6 =0.3 L=10


Example 5 2


1 Femap 11 is used

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Example 5 3

I. Defining Materials and Properties Model>Material...

Remark: In a message window at the bottom of the screen, you can see a confirmation that material is created. After FEMAP displays dialog box Define Isotropic Material press Cancel.

Model>Property...

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Example 5 4

Generation of the second property.


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Example 5 5



After FEMAP displays again dialog box Locate Enter Coordinates or Select with Cursor press 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 5 6

Model>Element... (Ctrl+E) The following dialogue box appears.



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Example 5 7

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Example 5 8

Model>Constraint>Nodal... Note: Graphically (using mouse) pick the location of nodes in which constraints are given (3) on screen, Fig. 2. It will be marked by +3 and added to Entity Selection box, so it could not be selected (marked) again.

Now, select nodes 1 and 2.

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Example 5 9


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Example 5 10


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Example 5 11

Model>Load>Nodal... Force at node 1 should be specifying.


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Example 5 12


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Click on a Add button do define second line, Edit Series dialog are opened.

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Example 6 1

EXAMPLE 6. (SG_4) Large displacements of circle arc Description/Objective Circle arc having unsymmetrical supports is loaded by force (Fig. 1). Force increase 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


Example 6 2


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Example 6 3

I. Defining Materials and Properties Model>Material...

After FEMAP displays dialog box Define Isotropic Material press Cancel.

Model>Property...

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Example 6 4

After FEMAP displays again dialog box Define Property - MEMBRANE Element Type press Cancel.

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Example 6 5

II. 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.

After FEMAP displays again dialog box Locate Enter Location at Center of Arc press Cancel. Adjustment of a view of whole drawing at the screen with command:

View>Autoscale>Visible (short-cut key Ctrl+A) A following figure is now shown at the screen, Fig. 2.

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Example 6 6

Fig. 2

Let's define a surface between created arcs.

Geometry>Surface>Ruled...

After FEMAP displays again dialog box Create Ruled Surface press 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

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Example 6 7

III. 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.

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

Mesh>Geometry>Surface... (short-cut key Shift+F11)

To reduce the amount of information displayed (turn off geometry), use the FEMAP View Visibility Options (short-cut key Ctrl+Q):

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Example 6 8

Display labelling of nodes and elements by ID View>Options... (short-cut key F6) The following dialogue box appears.

Finite element model is shown in the Fig 4.

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Example 6 9

Fig. 4

IV. Constraining the Model Note: Since Constraints are Set based, you must create an empty Constrain Set before defining any actual constrains. Model>Constraint>Create/Manage Set... (short-cut key Shift+F2)

1


Example 6 10

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

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

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Example 6 11

Modify>Update other>Perm Constraint...

V. Loading the Model Note: Since Load are Set based, you must create an empty Load Set before defining any actual load. Model>Load>Create/Manage Set... (short-cut key Ctrl+F2)

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Example 6 13

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

Fig. 5


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VI. Prepare and Submit the Model for a Nonlinear Analysis Create the input file and solve the model. Click on a PAK in main menu to start PAK translator. Pak translator should automatically create new DAT file and start PAK solver.


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VI Postprocessing and Review the Results FEMAP can display displacements in y direction of model as following: View>Select... (short-cut key F5)

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After FEMAP displays again dialog box Select PostProcessing Data press OK. After FEMAP displays again dialog box View Select press OK. Througout a few steps from Post Toolbar and Entity Display Toolbar shown bellow, you can setup appropriate view of your results on the screen. Post Toolbar

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Example 6 18

Entity Display Toolbar

Real deformation in 50th step is now shown at the screen, together with undeformed (original) model, Fig. 6.

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Let's plot force-displacement diagram at node 16 at which load is given. FEMAP can generate XY plots of results using the Charting dockable pane. There are two different entities in the Charting pane, Charts and Data Series. Any number of Chart entities may exist in the model and each Chart may display any number of selected Data Series. The Type of Data Series determines what will be displayed in the selected Chart. In addition, each Type of Data Series requires specific input to properly create the XY plot. If the Charting pane is already displayed, skip this step...



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Select values of the second column; the references of the

nonlinear analysis femap

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