Download - MSC Nastran - Basic Analysis

BA

SIC A

NA

LY

SIS

eans d to that

ing's

tic ay

state ,

for lied

mpute

1

This chapter describes the analysis capabilities of Basic Structural Analysis: linear static analysis, buckling analysis, and normal modes analysis. This chapter is divided into the following sections:

4.1 Linear Static Analysis

4.2 Normal Modes Analysis

4.3 Buckling Analysis

4.4 Thermal Loading

Each section concludes with a detailed step-through example.

4.1 Linear Static AnalysisLinear static analysis represents the most basic type of analysis. The term “linear” mthat the computed response—displacement or stress, for example—is linearly relatethe applied force. The term “static” means that the forces do not vary with time—or, the time variation is insignificant and can therefore be safely ignored.

An example of a static force is a building's dead load, which is comprised of the buildweight plus the weight of offices, equipment, and furniture. This dead load is often expressed in terms of lb/ft2 or N/m2. Such loads are often defined using a maximum expected load with some factor of safety applied for conservatism.

In addition to the time invariant dead load described above, another example of a staload is an enforced displacement. For example, in a building part of the foundation msettle somewhat, inducing static loads. Another example of a static load is a steady-temperature field. The applied temperatures cause thermal expansion which, in turncauses induced forces.

The static analysis equation is:

[K]{u} = {f}

where [K] is the system stiffness matrix (generated automatically by MSC/NASTRANWindows (MSC/N4W), based on the geometry and properties), f is the vector of appforces (which you specify), and u is the vector of displacements that MSC/NASTRANcomputes. Once the displacements are computed, MSC/NASTRAN uses these to coelement forces, stresses, reaction forces, and strains.

Basic Analysis 4

4-2 Basic Analysis4
The applied forces may be used independently or combined with each other. The loads can also be applied in multiple loading subcases, in which each subcase represents a particular loading or boundary condition. Multiple loading subcases provide a means of solution efficiency, whereby the solution time for subsequent subcases is a small fraction of the solution time for the first, for a particular boundary condition.
4.1.1 Flat Plate with a Single LoadExample exercise for Linear Static Analysis.

Model Description:In this example we create a 4 in. square plate with filleted edges (0.5 in. fillet radius) and a 2 in. diameter circular hole in the center. The plate is made of steel, 0.1 in. thick. The model is simply supported around the outer edge, and a 10g gravity load is applied normal to the plate. The plate is modeled with flat plate elements. Nodal displacements and element stresses are computed.

This example uses English units: inches (in.) for length, pounds (lb) for force, and seconds (sec) for time. Note that MSC/N4W assumes a consistent set of units, so you need to be consistent and not mix units (i.e., do not mix feet and inches).

Follow the steps described starting on the next page to create the geometry, finite element mesh, loads and constraints.

Exercise Procedure:1. Start up MSC/NASTRAN for Windows 4.0 and begin to create a new model.

Start MSC/N4W by double-clicking on the MSC/N4W icon. When the Open Model File dialog box appears; choose New Model.

2. Create a 4 in. Square.

Open Model File: New Model

4-3 Flat Plate with a Single LoadB

AS

IC AN

AL

YS

IS

4
Model the geometry of this exercise.
Locate - Enter First Corner of Rectangle

Locate - Enter Diagonally Opposite Corner of Rectangle

The rectangle may be displayed in the corner of the display window. If so, you can resize and center the display by choosing View/Autoscale (or pressing Ctrl+A).

Geometry/Curve-Line/Rectangle...

X: 0 Y: 0 Z: 0

OK

X: 4 Y: 4 Z: 0

OK

View/Autoscale

4-4 Basic Analysis4

3. Display the Curve Labels and Turn Off Workplane Rulers.

The default for the curve and other geometry labels is to be turned off. We will turn them on here, however, to assist in subsequent operations.

To turn them on, choose View/Options, which brings up a dialog box. Select Labels, Entities and Color in the Category box.

Choose Curve from the Options box, which brings up additional small boxes to the right of the Options box. In the Label Mode box, select ID to display curve identifier numbers.

View/Options...

Category: l Labels, Entities and Color

Options: Curve

Label Mode: 1..ID


AS

IC AN

AL

YS

IS

4

Then choose Apply to apply the labels.

Now select Tools and View Style in the Category box. Choose Workplane and Rulers and uncheck the Draw Entity check box.

Apply

Category: l Tools and View Style

Options: Workplane and Rulers

Draw Entity

4-6 Basic Analysis4

Then choose OK to apply these changes and exit the View Options box.

4. Fillet the Corners.

To fillet the corners choose Modify/Fillet, which brings up the Fillet Curves dialog box.

OK


AS

IC AN

AL

YS

IS

4
Enter 0.5 for the fillet Radius. To fillet the corner between curves 1 and 2, enter 1 for Curve 1 and 2 for Curve 2; then, to indicate the fillet direction, enter 3 for X and 1 for Y to define an approximate fillet center of 3,1; then choose OK.
With Center Near:With Center Near:

Modify/Fillet...

Curve 1: 1

Curve 2: 2

Radius: 0.5

X: 3 Y: 1 Z: 0

OK

4-8 Basic Analysis4
Fillet the upper right corner with the following:
With Center Near:

Fillet the upper left corner with the following:

With Center Near:

Fillet the lower left corner with the following:

With Center Near:

Exit the Fillet Curves box by choosing Cancel.

Curve 1: 2

Curve 2: 3

Radius: 0.5

X: 3 Y: 3 Z: 0

OK

Curve 1: 3

Curve 2: 4

Radius: 0.5

X: 1 Y: 3 Z: 0

OK

Curve 1: 4

Curve 2: 1

Radius: 0.5

X: 1 Y: 1 Z: 0

OK

Cancel


AS

IC AN

AL

YS

IS

4

5. Create the Center Hole.

To create the center hole choose Geometry/Curve-Circle/Center, which brings up a dialog box.

Locate - Enter Location at Center of Circle:

Geometry/Curve-Circle/Center...

X: 2 Y: 2 Z: 0

OK

Radius: 1

4-10 Basic Analysis4

se

file. o a

The display should be as follow:

6. Save the Geometry.

It is recommended that, after numerous steps in building a complex model, you save your model file. While the steps so far are not numerous—nor is the model complex—it isinstructive, nevertheless, to illustrate how to save the model.

To save your model, choose File/Save; the Save As dialog box appears (“save as” becauthe file has not yet been saved). Enter plate1.mod for File Name and press Save to save the file as plate1.mod. Note that “mod” is the default filename extension for a model Note, too, that this filename is now shown on the MSC/N4W title bar. Next time you dsave of this model the updated model file will be saved with the same name.

OK

Cancel

File/Save

File Name: plate1

Save


AS

IC AN

AL

YS

IS

4
7. Creating the Material Properties.
Now that we have created the basic geometry we will create the properties, beginning with the material properties.

Choose Model/Material, which brings up the Define Isotropic Material dialog box. (Note that the default material type is isotropic.)

To read the material properties, choose Load, which brings up the Select Entity box.

Select AISI 4340 Steel and note that the isotropic material properties are entered in the Isotropic Material box. Note that the density is mass density, which is in units of lb-sec2/in.4 for English units. Note, too, that the material ID is 1.

Model/Material...

Load...


8. Creating the Element Properties.

Next we create element properties. Choose Model/Property to bring up the Define Property--PLATE Element Type box. (Note that the default element type is plate elements.)

9. Generating the Mesh.

Library Entry: AISI 4340 Steel

OK

OK

Cancel

Model/Property...

Title: Plate Property

Material: 1..AISI 4340 Steel

Thicknesses, Tavg or T1: 0.1

OK

Cancel


AS

IC AN

AL

YS

IS

4
After we define the engineering properties we create the element mesh. First, choose Mesh/Mesh Control/Default Size, which brings up a dialog box.
Then sets a mesh size of 0.4 in. for each plate element.

Next, choose Geometry/Boundary Surface to select the boundaries of the mesh. This brings up the Entity Selection box.

The boundary surface is now defined.

Mesh/Mesh Control/Default Size...

Size: 0.4

OK

Geometry/Boundary Surface...

Select All

OK


Next, choose Mesh/Geometry/Surface and pick the boundary surface that has just been created.

Select Surface 1.

The Automesh Surface dialog box will appear next.

Mesh/Geometry/Surface...

OK


AS

IC AN

AL

YS

IS

4

When meshing is completed, 135 elements and 163 nodes are generated.

10. Modifying the Display

In order to better view the model, certain entities can be turned off for clarity. Choose View/Options.

Property: 1..Plate Property

OK

View/Options...

Category: l Labels, Entities and Color

Options: Point

Draw Entity

Apply

Options: Curve

Draw Entity

Apply


The geometry (curves and points) and boundaries are now turned off.

The filled dot at the origin can also be turned off.

Options: Boundary

Draw Entity

Apply


Options: View Legend

Draw Entity

Options: View Axes

Draw Entity

Options: Origin

Draw Entity

OK


AS

IC AN

AL

YS

IS

4
11. Creating the Boundary Conditions.
First, choose Model/Constraint/Set and enter the load set title.

Next, we apply pinned supports to the outer edge.

Model/Constraint/Set...

Title: Simply Supported

OK

Model/Constraint/Nodal...

ID: 1 to: 40

OK

Pinned


Pinned supports are applied to nodes 1 through 40 (the outer edge).

12. Creating the Applied Load.

Next, we model a 10g load applied normal to the plate.

Apply an acceleration of -3864 for Z. (This defines a steady-state acceleration of 3864 in./sec2--10g--in the -Z direction, which is normal to the plate.)

OK

Cancel

Model/Load/Set...

Title: 10g gravity load

OK

Model/Load/Body...

Active Acceleration

Translation/Gravity (length/time/time) Z: -3864


AS

IC AN

AL

YS

IS

4

13. Performing the Linear Static Analysis.

We are now ready to analyze a model. Choose File/Analyze, which brings up the Analysis Control box.

OK

File/Analyze...

Run Analysis

OK

When prompted, “OK to Save Model Now?” Select Yes. The analysis can run for several minutes, depending on the speed of your PC.
14. Processing the Results.

After the analysis is complete, you are then prompted for the Message Review, click Continue.

At this stage the results have already been read into the database ready for processing.

15. Modifying the Display with quick options.

Turn off the constraint entities and labels.

Choose View Options, select Quick Options.

16. Plotting Stress Contours.

Choose View/Select, which brings up a dialog box, and plot the Von Mises Stress.

Yes

Continue

View/Options...

Quick Options...

Draw: Constraint

Done

OK

View/Select...

Contour Style: l Contour


AS

IC AN

AL

YS

IS

4

Deformed and Contour Data...

Output Vectors / Contour: 7033..Plate Top VonMises Stress

OK

OK


17. Plotting the Deformed Shape.

Choose View/Select and turn off Contour by selecting None - Model Only under Contour Style. Select Deform under Deformed Style. Choose Deformed and Contour Data, and under Output Vectors, Deformation scroll down and select T3 Translation (which is Z translation).

Note that the deformed shape is plotted in white and is overlaid on the undeformed (blue) shape. The deformation can better be viewed by rotating the model. Choose View/Rotate and select Isometric. The model is rotated such that the deformation can be seen.

View/Select...

Deformed Style: l Deform

Contour Style: l None-Model Only


Output Vectors / Deformation: 4..T3 Translation

OK

OK

View/Rotate...


AS

IC AN

AL

YS

IS

4

y

18. Animating the Deformation.

The deformation can be animated.

Choose View/Select, and under Deformed Style choose Animate.

The animation may be a little fast but can be slowed down by selecting View/Advanced Post/Animation and clicking Slower. The animation continues until another menu—anmenu—is selected.

Isometric

OK

View/Select...

Deformed Style: l Animate

OK

View/Advanced Post/Animation...

Slower (Click until the model moves at the desired speed)

OK

19. Plotting Deformation Contours.
20. Exiting the Program

To exit, choose File/Exit and choose Yes to save the current model, plate1.mod, and its results.

View/Select...

Deformed Style: l None - Model Only



Output Vectors / Contour: 4..T3 Translation

OK

OK

File/Exit

Yes

4-25 Normal Modes AnalysisB

AS

IC AN

AL

YS

IS

4

4.2 Normal Modes AnalysisNormal modes analysis computes the natural frequencies and mode shapes of a structure. The natural frequencies are the frequencies at which a structure will tend to vibrate if subjected to a disturbance. For example, the strings of a piano are each tuned to vibrate at a specific frequency. The deformed shape at a specific natural frequency is called the mode shape. Normal modes analysis is also called real eigenvalue analysis.

Normal modes analysis forms the foundation for a thorough understanding of the dynamic characteristics of the structure. Normal modes analysis is performed for many reasons, among them:

❍ Assessing the dynamic interaction between a component (such as a piece of rotatingmachinery) and its supporting structure; if the natural frequency of the supportingstructure is close to an operating frequency of the component then there can besignificant dynamic amplification of the loads.

❍ Assessing the effects of design changes on the dynamic characteristics.

❍ Using the modes in a subsequent forced response analysis.

❍ Using the natural frequencies as a guide to selecting the proper time or frequency stepfor transient and frequency response analyses, respectively.

❍ Assessing the degree of correlation between modal test data and analytical results.

In normal modes analysis there is no applied load and the structure has no damping properties. The equation of motion is of the form:

[M]{u} + [K]{u} = 0

where [K] and [M] are the stiffness and mass matrices representing the elastic and inertial properties of the structure respectively. These system matrices are generated automatically by MSC/NASTRAN, based on the geometry and properties of the FE model.

Assuming a harmonic solution, the above reduces to an eigenvalue problem.

where {φ} is the eigenvector (or mode shape) corresponding to the eigenvalue λ (the natural or characteristic frequency). For each eigenvalue, which is proportional to a natural frequency, there is a corresponding eigenvector, or mode shape. The eigenvalues are related to the natural frequencies as follows:

Each mode shape is similar to a static displaced shape in that there are displacements and rotations for each node. However, there is one important difference between the mode shape and the static displacements: the scaling. In static analysis the displacements are the true physical displacements due to the applied loads. Since there is no applied load in normal mode analysis, the mode shape components can all be scaled by an arbitrary factor. With MSC/NASTRAN this scaling can be done so that the maximum displacement in any

K λi– M φi{ } 0=

fi λi 2π⁄=


gh data.

as for nts. Due mode

ods

wer

as ree, or

sis.

mode is 1.0. Another option is to allow any user specified degree of freedom have a modal displacement of 1.0. The first option—unit modal mass—is generally preferred, thouthe scaling of a maximum displacement to 1.0 is useful for comparison to modal test

Element forces and stresses and reaction forces are computed in the same manner static analysis, with each mode shape treated the same as a set of static displacemeto the scaling of each mode, the resulting element stresses and forces are on a per basis and cannot necessarily be compared from one mode to another.

Because no single eigenvalue extraction method is perfect for all models, we have incorporated several methods in MSC/NASTRAN. These eigenvalue extraction methare:

❍ Lanczos method

❍ Givens method

❍ Householder method

❍ Modified Givens method

❍ Modified Householder method

❍ Inverse power method

❍ Sturm modified inverse power method

The Lanczos method is the best overall method due to its robustness, but the other methods (particularly the modified Givens method and the Sturm modified inverse pomethod) have applicability for particular cases.

MSC/NASTRAN's eigenvalue methods can also analyze unrestrained models, suchthose that arise from aircraft in flight. These unrestrained models give rise to stress frigid body modes, which MSC/NASTRAN can analyze without any special modeling analysis techniques.

4.2.1 Bracket ModelExample exercise for Normal Modes Analysis.

Model Description:In this example we use a model created previously to perform a normal modes analy

4-27 Bracket ModelB

AS

IC AN

AL

YS

IS

4

ties,

alyzed

The model file is basically complete for analysis—all of the nodes, elements, properand constraints are included.

Exercise Procedure:1. Start up MSC/NASTRAN for Windows 4.0 and read in the model.

Start MSC/N4W by double-clicking on the MSC/N4W icon. When the Open Model File dialog box appears; find and choose bracket.mod.

Change to the examples directory. (This is a database containing the model to be anin this example.)

Open Model File: bracket.mod

Open


2. Save the model.

Since we will edit this database for our example, save the model as bracket1.mod by choosing File/Save As.

The view can be cleaned up by switching off the geometry in the View Quick Options dialog box by selecting Ctrl+Q or through the View/Options/Quick Options menu.

3. Review the model.

Note the size and uniformity of the mesh between the arcs at the top of the bracket. This was accomplished by explicitly defining parameters for the number of elements on these arcs.

File/Save As...

File Name: bracket1

Save

View/Options...

Quick Options...

Geometry Off

Done

4-29 Bracket ModelB

AS

IC AN

AL

YS

IS

4

Controlling the mesh parameters is a useful way to minimize the total number of elements in the mesh. This improves analysis job performance. Controlling mesh parameters also enables analysts to enhance the shape of mesh elements. Improving the shape on mesh elements increases the reliability of analysis results.

To review the mesh parameters used on this model select Mesh/Mesh Control/Size - Along Curve from the Mesh Menu.

Select the arc at the top of the bracket (arc 2) and the one at the top of the slot (arc 17).

The number of elements selected should be set to a reasonable number in order to create well shaped elements. For this example we will select 6 elements around the 180 degree arc, giving a maximum included angle of 30 degrees or less for each element. Specifying the same number of elements on these concentric arcs will ensure a uniform mesh between the upper arc and the top of the slot.

4. Performing the Normal Mode Analysis.

We are now ready to analyze a model. Choose File/Analyze, which brings up the Analysis Control box. Prepare an Normal Modes analysis for the lowest three resonant frequencies and mode shape.

Mesh/Mesh Control/Size Along Curve...

OK

l Number of Elements 6

OK

Cancel

File/Analyze...


When prompted, “OK to Save Model Now?” Select Yes. The analysis can run for several minutes, depending on the speed of your PC.

5. Processing the Results.

After the analysis is complete, you are then prompted for the Message Review, click Continue.

At this stage the results have already been read into the database ready for processing.

6. Creating Multiple Views.

Because we have 3 modes it is convenient to create 3 views for plotting the deformed shapes. To do so:

A. Create 3 viewports.

Analysis Type: 2..Normal Modes/Eigenvalue

Number of Modes 3

Run Analysis

OK

Yes

Continue

View/New...

Create Layout: l 3

4-31 Bracket ModelB

AS

IC AN

AL

YS

IS

4

Three views are drawn, each in a different window and orientation.

The large window on the right and the lower left window are XY views and will not be changed. To rotate the upper left window to an Isometric view, do the following:

B. Select the upper left window by clicking anywhere in its window. Select from the main menu View/Rotate.

It is now put in the Isometric view.

C. Follow step B but change the lower left window to XY Top view.

D. The views need to be cleaned up to remove labels and switch off the workplane rul-ers. To do so:

Press Ctrl+Q for View Quick or:

OK

View/Rotate...

Isometric

OK

View/Option...

Quick Options...

Turn off everything except Element and Constraint markers.
E. Then select View/Options and pick the Tools and View Style category. Then pick Workplane and Rulers and deselect the Draw Entity checkbox. Finally select OK.

Your windows should appear as follows.

(upper right corner) All Views

All Entities Off

Labels Off

Draw: Element

Draw: Constraint

Done

View/Option...


Options: Workplane and Rulers

(upper right corner) Draw Entity

OK

4-33 Bracket ModelB

AS

IC AN

AL

YS

IS

4
7. Display the results.
To display the first mode on the upper left view, click on upper left viewport.

The deformed shape for the first mode is now displayed over the undeformed model.

Next, display the second mode shape as a contour plot. Click on the lower left viewport.

View/Select...

(upper right corner) All Views


Contour Style: l None - Model Only


Output Set: 1..Mode 1 xxx.xx Hz

OK

OK

View/Select...





Output Vectors/Contour: 1..Total Translation

OK

OK

The deformed shape for the third mode is now displayed over the undeformed model.
Finally, create a contour plot of the third mode and then animate it. To do so, click on V2 viewport (right hand side).

These operations create the deformation contour plot for the third mode.

View/Select...





Output Vectors/Contour: 1..Total Translation

OK

OK

4-35 Bracket ModelB

AS

IC AN

AL

YS

IS

4

To animate the plot, select View/Options, and then select PostProcessing for the Category and Animated Style for the Options.

Change Frames to 5. Because the animation is done by creating multiple frames of scaled deformation, an odd number of frames creates a frame that of zero deformation.

View/Option...

Category: l PostProcessing

Options: Animated Style

Shape: 4..Sine - Full

Frames: 5


ge as
Click the Animate checkbox to change the contour levels as the model is animated. (Note that in the first example—the plate with a single load case—the contour did not chanthe model was animated.)
Apply

Options: Contour/Criteria Levels

Animate

4-37 Bracket ModelB

AS

IC AN

AL

YS

IS

4

Rotate the model and start the animation.

Five frames are drawn and the model is animated.

The animation speed can be changed with View/Advanced Post/Animation.

OK

View/Rotate...

Isometric

OK

View/Select...

Deformed Style: l Animate

OK

View/Advanced Post/Animation...


the

s the d

s d that

her-ype, linear d

Note that as you click on Slower do so, the Delay increases. (The delay is proportional to the amount of time that the computer “waits” between frames—the larger the delay, slower the apparent animation speed.)

Press Next> several times—that performs frame-by-frame stepping in the forward direction. (<Prev does likewise, though in the reverse direction.)

Stop the animation by choosing View/Select, setting Deformed Style to Deform.

8. Exiting the Program

To exit, choose File/Exit and choose Yes to save the current model and its results.

4.3 Buckling AnalysisIn linear static analysis, a structure is assumed to be in a state of stable equilibrium. Aapplied load is removed, the structure is assumed to return to its original, undeformeposition. Under certain combinations of loadings, however, the structure continues todeform without an increase in the magnitude of loading. In this case the structure habecome unstable; it has buckled. For elastic, or linear, buckling analysis, it is assumethere is no yielding of the structure and that the direction of applied forces does not change.

Elastic buckling incorporates the effect of the differential stiffness, which includes higorder strain displacement relationships that are functions of the geometry, element tand applied loads. From a physical standpoint, the differential stiffness represents aapproximation of softening (reducing) the stiffness matrix for a compressive axial loaand stiffening (increasing) the stiffness matrix for a tensile axial load.

Slower (Click until the model moves at the desired speed)

OK

View/Select...


OK

File/Exit

Yes

4-39 Link ModelB

AS

IC AN

AL

YS

IS

4
In buckling analysis we solve for the eigenvalues that are scale factors that multiply the applied load in order to produce the critical buckling load. In general, only the lowest buckling load is of interest, since the structure will fail before reaching any of the higher-order buckling loads. Therefore, usually only the lowest eigenvalue needs to be computed.
The buckling eigenvalue problem reduces to:

where K is the system stiffness matrix, Kd is the differential stiffness matrix (generated automatically by MSC/NASTRAN, based on the geometry, properties, and applied load), and are the eigenvalues to be computed. Once the eigenvalues are found the critical buckling load is solved for:

where Pcr are the critical buckling loads and Pa are the applied loads. Again, usually only the lowest critical buckling load is of interest.

Because no single eigenvalue extraction method is perfect for all models, we have incorporated three methods in MSC/NASTRAN:

❍ Lanczos method

❍ Inverse power method

❍ Sturm modified inverse power method

The Lanczos method is the best overall method because it provides the most accuracy for the least cost, but the other methods have applicability for particular cases.

4.3.1 Link ModelExample exercise for Buckling Analysis.

Model Description:The purpose of this problem is to investigate the linear buckling analysis process by conducting a simple buckling analysis on an existing link model (which is in the form of a FEMAP neutral file). In this analysis we will use the existing plate geometry and finite element mesh and apply the necessary loads and boundary conditions to determine the buckling load and buckled shape of the link.

Exercise Procedure:1. Start up MSC/NASTRAN for Windows 4.0.

Start MSC/N4W by double-clicking on the MSC/N4W icon. When the Open Model File dialog box appears; select New Model.

Open Model File: New Model

K λi+ Kd 0=

λi

Pcri λiPa=

2. Import the FEMAP neutral file, link.neu.
Change to the examples directory. (This is a database containing the model to be analyzed in this example.

3. Save the model.

Once the file has been read in it is good practice to rename it, select File/Save As and enter the name Link in the File name box.

File/Import/Analysis Model...

Analysis Format: l FEMAP Neutral

OK

File Name: link.neu

Open

OK

File/Save As...

File Name: Link

Save

4-41 Link ModelB

AS

IC AN

AL

YS

IS

4
Since the geometry and mesh already exist, in this example we will concentrate on the aspects directly related to buckling analysis. To accomplish this, we will create new boundary conditions and applied loads and use these for the buckling analysis.
4. Change the title on the window.

The graphics window now has a problem specific title.

5. Creating New Boundary Conditions.

Select Model/Constraint/Nodal and enter Buckling Boundary Cond. for the constraint set title.

View/Window...

Title: Plate Buckling

OK

Model/Constraint/Nodal...

Title: Buckling Boundary Cond.

OK

The Entity Selection dialog box then appears. Use the cursor to select the nodes around the hole on the lower part of the model (node 138-153) and fix all translational DOF on these nodes.
6. Creating the Buckling Loading Condition

With the boundary conditions specified, we now create the loading configuration for which the buckling load will be calculated. In this problem, we will simulate the application of a uniform load applied at the upper hole with a set of concentrated nodal forces. Since the result of the buckling analysis is a buckling load factor, for simplicity we apply unit load values. We apply the loading such that the link is being placed in planar compression in the negative Y direction. Other configurations could easily be considered.

ID: 138 to: 153

OK

Pinned

OK

Cancel

Model/Load/Nodal...

Title: In Plane Loading

4-43 Link ModelB

AS

IC AN

AL

YS

IS

4

The Select Nodes dialog box then appears, select the nodes around the bottom of the hole (nodes 178 and 184-189).

When the Create Loads on Nodes dialog box appears, enter a magnitude of -1.0 in the FY box. We choose a magnitude of 1.0 to represent a simple unit load. The minus sign is used to orient the load so as to apply a compressive load to the plate.

OK

ID: 178 to: More

ID: 184 to: 189

OK

FY -1


7. Modifying the Display.

To clean up the display of the model the geometry entities and boundary condition and loading labels can be turned off.

Press Ctrl+Q for View Quick or:

Turn off geometry and boundary condition.

OK

Cancel

View/Option...

Quick Options...

Geometry Off

Labels Off

Draw: Load - Force

Draw: Constraint

Done

4-45 Link ModelB

AS

IC AN

AL

YS

IS

4

8. Saving and Analyzing the Model

With the loading and boundary conditions defined for the buckling analysis we are now ready to analyze the link for its buckling load. Before we do this it is a good idea to save the model in its current state by choosing File/Save.

We can now select File/Analyze and prepare for a Buckling analysis.

File/Save

File/Analyze...

Analysis Type: 7..Buckling

Run Analysis


The analysis then starts. When it has completed, the results are read into the database and are ready for postprocessing.

9. Preparing for Postprocessing

Once the analysis has completed the results are read in automatically. A Message Review dialog box appears and as long as there are no Fatal errors, the Continue button can be selected.

Select View/Rotate and choose Dimetric in the dialog box.

OK

yes

Continue

File/Rotate...

Dimetric

OK

4-47 Link ModelB

AS

IC AN

AL

YS

IS

4

10. Postprocessing the Analysis Results

The important results of a buckling analysis are typically the buckling load factor (eigenvalue) and the buckled shape.

To access the analysis results choose View/Select. In the View Select dialog box, choose Deform for the Deformed Style and Full Hidden Line for the Model Style. These choices will create a hidden line plot of the deformed (buckled) shape superimposed over the undeformed shape.

View/Select...

Model Style: l Full Hidden Line



Select the Deformed and Contour Data... button to activate the buckling results. In the Select PostProcessing Data dialog box select the Output Set for Eigenvalue 1. In our case it is set "2..Eigenvalue 1 36.351". (Depending upon the sequence you have used in accessing the different analysis capabilities demonstrated using this problem your set number may be different.) For the Output Vectors, select 1..Total Translation in the Deformation box using the scroll bar to the right of the box.


Output Set: 2..Eigenvalue 1 36.351

Output Vectors/Deformation: 1..Total Translation

4-49 Link ModelB

AS

IC AN

AL

YS

IS

4

11. Rotate the model for a better view of the result.

OK

OK

View/Align By/Dynamic...


Holding down the left mouse button and dragging the cursor. Drag left or right to rotate the model about the y axis.

Drag up and down to rotate about the x axis.

Select Cancel to return the model to the original Isometric View when you are done.

12. Calculate the Buckling Load

To calculate the total buckling load we first have to obtain a summation of the forces in the system. Choose Tools/Check/Sum Forces, activating the following dialog box:

Since in this problem we are only interested in the summation of the forces in the Y direction, the origin (X = 0, Y = 0, Z = 0) is a reasonable point about which to sum the forces. This choice creates a Summation of Forces Table in the Messages and Lists window.

l Rotate XY

Cancel

Tools/Check/Sum Forces...

X: 0 Y: 0 Z: 0

OK

4-51 Thermal LoadingB

AS

IC AN

AL

YS

IS

4

d.

and

hese

d at

by rform

This table shows that the total load we’ve applied in the Y direction is -7.0 lbs. To calculate the buckling load, we multiply the applied load by the buckling load factor (eigenvalue) or:

Applied Load x Buckling Load Factor = Buckling Load

- 7.0 lbs x 36.35 = - 254.45 lbs

More directly stated, the link will buckle at a total load of 254.45 lbs, uniformly distributed along the edge of the hole.

The buckling load factor is a scale factor whose value is a function of the applied loaHad we applied a load set that was 100 times greater (100 lbs instead of 1.0 lb) the resulting computed buckling load factor would be proportional to the increased load would be 0.3635, resulting in the same total buckling load.

Additional postprocessing (i.e., contours, XY plots, etc.) can easily be performed on tresults.

4.4 Thermal Loading

4.4.1 Lug with a Thermal LoadWe will create an aluminum lug with geometry shown in the figure. The lug is attachethe base to a larger component that has generated heat. The thermal loading will bemodeled as a linear temperature distribution from the base.

Example exercise for Thermal Loading.

Model Description:This example will demonstrate how to create 3D geometry, automesh solid elementsextruding, generate a nodal temperature distribution using built-in equations, and pegraphical post-processing on solid elements.

Download - MSC Nastran - Basic Analysis

Top Related