# msc nastran - basic analysis

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Nastran

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• 14.1

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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 Analysis4.2 Normal Modes Analysis4.3 Buckling Analysis4.4 Thermal Loading

Each section concludes with a detailed step-through example.

Linear Static AnalysisLinear static analysis represents the most basic type of analysis. The term linear means that the computed responsedisplacement or stress, for exampleis linearly related to the applied force. The term static means that the forces do not vary with timeor, that 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 building's weight 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 static load is an enforced displacement. For example, in a building part of the foundation may settle somewhat, inducing static loads. Another example of a static load is a steady-state temperature field. The applied temperatures cause thermal expansion which, in turn, causes induced forces.

The static analysis equation is:

[K]{u} = {f}where [K] is the system stiffness matrix (generated automatically by MSC/NASTRAN for Windows (MSC/N4W), based on the geometry and properties), f is the vector of applied forces (which you specify), and u is the vector of displacements that MSC/NASTRAN computes. Once the displacements are computed, MSC/NASTRAN uses these to compute element forces, stresses, reaction forces, and strains.

asic Analysis 4

• 4-2 Basic Analysis4The 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

4.1.1

Mode

Exercsolution time for the first, for a particular boundary condition.

Flat Plate with a Single LoadExample exercise for Linear Static Analysis.

l 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.

ise 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 Load 4Model the geometry of this exercise.

Geometry/Curve-Line/Rectangle...BA

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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).

X: 0 Y: 0 Z: 0

OK

X: 4 Y: 4 Z: 0

OK

View/Autoscale

• 4-4 Basic Analysis43. 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

• 4-5 Flat Plate with a Single Load 4

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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 Analysis4Then 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

• 4-7 Flat Plate with a Single Load 4Enter 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.BA

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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 Analysis4Fillet the upper right corner with the following:

Curve 1: 2With 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 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

• 4-9 Flat Plate with a Single Load 4

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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 Analysis4The 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 numerousnor is the model complexit is instructive, nevertheless, to illustrate how to save the model.

To save your model, choose File/Save; the Save As dialog box appears (save as because the 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 file. Note, too, that this filename is now shown on the MSC/N4W title bar. Next time you do a save of this model the updated model file will be saved with the same name.

OK

Cancel

File/Save

File Name: plate1

Save

• 4-11 Flat Plate with a Single Load 47. Creating the Material Properties.Now that we have created the basic geometry we will create the properties, beginning with the material properties.BA

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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...

• 4-12 Basic Analysis4

Library Entry: AISI 4340 Steel8. 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.

OK

OK

Cancel

Model/Property...

Title: Plate Property

Material: 1..AISI 4340 Steel

Thicknesses, Tavg or T1: 0.1

OK

Cancel

• 4-13 Flat Plate with a Single Load 4After we define the engineering properties we create the element mesh. First, choose Mesh/Mesh Control/Default Size, which brings up a dialog box.BA

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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

• 4-14 Basic Analysis4Next, 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

• 4-15 Flat Plate with a Single Load 4

Property: 1..Plate PropertyBA

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

10. Modifying the DisplayIn order to better view the model

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