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In earlier chapters, you have learned about performing the static analysis of various components and assemblies. In this chapter, you will learn about performing the buckling analysis.

The buckling analysis is used to calculate the buckling load which is also known as the critical load. It is the load under which the model can start buckling even if the maximum stress developed in the model is within the yield strength of the material. Buckling refers to a larger deformation occurred due to the compressive axial loads acting on the structures such as long slender columns and thin sheet components, see Figure 6.1.

It clear from the above formula that the buckling load does not depend upon the compressive strength of the material. As a result, the structure can buckle or fail, even if the maximum stress developed in the structure is within the compressive yield strength of the material. Also, on increasing the length of the structure, the force required to buckle the structure gets reduced.

In SOLIDWORKS Simulation, you can perform the buckling analysis of a structure to calculate the minimum bucking load factor and its associated buckling mode shape, when the structure can buckle under the compressive axial loads.

In this case study, you will perform the buckling analysis of a Pipe Support, see Figure 6.2 and determine its minimum bucking load.

The Pipe Support is fixed at its bottom and the 9500 Newton compressive axial load is subjected on its top face, see Figure 6.3. The Pipe Support is made up of Alloy Steel material.

In this case study, you will run the buckling analysis of a Pipe Support and determine its buckling factor of safety under the applied compressive load. Also, you need to calculate the buckling load or critical load based on the buckling factor of safety.

2. Opening the Pipe Support

3. Starting the Buckling Study

4. Applying the Material, Fixture, and Load

5. Generating the Mesh

6. Defining the Buckling modes

7. Running the Buckling Analysis

8. Displaying the Buckling Factor of Safety

9. Calculating the Buckling Load or Critical Load

1. Login to the CADArtifex website (www.cadartifex.com) with your user name and password. If you are a new user, first you need to register on CADArtifex website as a student.

2. After login to the CADArtifex website, click on SOLIDWORKS Simulation > SOLIDWORKS Simulation 2018 . All resource files of this textbook appear in the respective drop-down lists.

3. Click on Case Studies > C06 Case Studies . The downloading of Co6 Case Studies file gets started. Once the downloading is complete, you need to unzip the downloaded file.

1. Start SOLIDWORKS, if not already started.

2. Click on the Open button in the Welcome dialog box or the Open tool in the Standard toolbar. The Open dialog box appears.

3. Browse to the location > SOLIDWORKS Simulation > Case Studies > C06 Case Studies > Case Study 1 . Next, select the Pipe Support and then click on the Open button in the dialog box. The Pipe Support is opened in SOLIDWORKS.

1. Click on the Simulation tab in the Simulation CommandManager . The tools of the Simulation CommandManager appear.

2. Click on the New Study tool in the Simulation CommandManager . The Study PropertyManager appears at the left of the graphics area.

3. Click on the Buckling button in the Advanced Simulation rollout of the Study PropertyManager to perform the buckling analysis, see Figure 6.4.

5. Click on the green tick-mark button in the PropertyManager. The Pipe Support Buckling Study is added in the Simulation Study Tree.

Now, you need to apply the material, fixture and load to the model. The procedures to apply the material, fixture, and load in the Buckling analysis are the same as in the static analysis.

1. Invoke the Material dialog box by clicking on the Apply Material tool in the Simulation CommandManager and then apply the Alloy Steel material. Next, close the dialog box.

2. Right-click on the Fixtures option in the Simulation Study Tree and then click on the Fixed Geometry tool in the shortcut menu appeared. The Fixture PropertyManager appears.

3. Rotate the model such that you can view the bottom face of the Pipe Support model and then select it to apply the Fixed Geometry fixture, see Figure 6.5. Next, click on the green tick-mark button in the PropertyManager.

4. Right-click on the External Loads option in the Simulation Study Tree and then click on the Force tool in the shortcut menu appeared. The Force/Torque PropertyManager appears.

5. Change the orientation of the model to isometric and then select the top semi-cylindrical face of the Pipe Support model to apply the load, see Figure 6.6.

6. Select the Selected direction radio button in the PropertyManager. The Face, Edge, Plane for Direction field appears.

7. Expand the FeatureManager Design Tree, see Figure 6.7. Next, click on the Top Plane as the reference plane to define the direction of force.

8. Click on the Normal to Plane button in the Force rollout of the PropertyManager and then enter 9500 as the axial load acting on the model, see Figure 6.8.

9. Select the Reverse direction check box in the Force rollout to reverse the direction of force downward, see Figure 6.9.

10. Click on the green tick-mark button in the PropertyManager. The specified compressive axial load is applied on the Pipe Support.

1. Generate the curvature-based mesh with the default mesh parameters by using the Create Mesh tool. Figure 6.10 shows the meshed model.

Now, you need to define the required number of buckling modes to be calculated by the program. By default, SOLIDWORKS Simulation calculates the first buckling mode of the model.

1. Right-click on the Pipe Support Buckling Study ( name of the study ) in the Simulation Study Tree and then click on the Properties tool in the shortcut menu appears, see Figure 6.11. The Buckling dialog box appears, see Figure 6.12.

2. Enter 5 in the Number of buckling modes field of the Options tab in the dialog box to calculate five different buckling safety factors and the associated buckling modes for the Pipe Support.

1. Click on the Run This Study tool in the Simulation CommandManager . The Pipe Support Buckling Study ( name of the study ) window appears which displays the progress of analysis. After the analysis completes, the Results folder is added in the Simulation Study Tree with the five different mode shapes, see Figure 6.13. By default, the Amplitude1 (-Res Amp - Mode Shape 1-) is activated in the Results folder. As a result, the first buckling mode shape of the model, which occurs first when the model starts buckling, appears in the graphics area, see Figure 6.14.

You can also display the remaining buckling mode shapes of the model by double-clicking on the respective option in the Results folder of the Simulation Study Tree.

Now, you need to display the buckling factor of safety of the Pipe Support.

1. Right-click on the Results folder in the Simulation Study Tree and then click on the List Buckling Factor of Safety tool in the shortcut menu appeared, see Figure 6.15. The List Modes dialog box appears, see Figure 6.16.

The List Modes dialog box displays the specified number of buckling modes and the associated buckling factor of safety of each mode. The first buckling load factor is always smaller than the other buckling load factors and for any given load, it occurs first. Therefore, you can calculate the buckling load or critical load when the model can start buckling by using the first buckling factor of safety.

If the buckling load factor is greater than 1, the design is considered to be safe. If the buckling load factor is equal to 1 then the buckling starts occurring in the design. If the buckling load factor is less than 1, the design is considered to be failure and the buckling occurs in the design.

Now, you need to calculate the buckling load when the Pipe Support start buckling.

Now, you need to save the model and its results.

1. Click on the Save tool in the Standard toolbar. The model and its results are saved in the location > SOLIDWORKS Simulation > Case Studies > C06 Case Studies > Case Study 1 .

In this case study, you will perform the buckling analysis of a long Beam, see Figure 6.17. Determine the bucking load or critical load when the Beam can start buckling.

The Beam is fixed at its bottom and the 14000 Newton compressive axial load is subjected on its top face, see Figure 6.18. The Beam is made up of AISI 304 steel material.

In this case study, you will run the buckling analysis of a beam and determine the buckling factor of safety of the beam under the applied compressive load. Also, you need to calculate the buckling load or critical load based on the buckling factor of safety of the beam.

2. Applying the Material, Fixture, and Load

3. Generating the Mesh

4. Running the Buckling Analysis

5. Displaying the Buckling Factor of Safety

6. Calculating the Buckling Load or Critical Load

1. Start SOLIDWORKS and then open the Beam model from the location > SOLIDWORKS Simulation > Case Studies > C06 Case Studies > Case Study 2 .

You need to download the C06 Case Studies file by logging to the CADArtifex website (www.cadartifex.com), if not downloaded earlier.

2. When the Beam model is opened in SOLIDWORKS, click on the Simulation tab in the Simulation CommandManager . The tools of the Simulation CommandManager appear.

3. Click on the New Study tool in the Simulation CommandManager . The Study PropertyManager appears at the left of the graphics area.

4. Click on the Buckling button in the Advanced Simulation rollout of the Study PropertyManager to perform the buckling analysis, see Figure 619.

6. Click on the green tick-mark button in the PropertyManager. The Beam Buckling Study is added in the Simulation Study Tree, see Figure 6.20. Also, the joints appear on the beam member in the graphics area, see Figure 6.21. It is because, SOLIDWORKS Simulation, automatically identifies the geometry as a beam and calculates its joints.

Now, you need to apply the material, fixture and load on the beam.

1. Invoke the Material dialog box by clicking on the Apply Material tool in the Simulation CommandManager and then apply the AISI 304 steel material. Next, close the dialog box.

2. Right-click on the Fixtures option in the Simulation Study Tree and then click on the Fixed Geometry tool in the shortcut menu appeared. The Fixture PropertyManager appears.

3. Select the yellow joints appeared at the bottom of the beam in the graphics area, see Figure 6.22. Next, click on the green tick-mark button in the PropertyManager. The Fixed Geometry fixture is applied at the bottom joint of the beam.

4. Right-click on the External Loads option in the Simulation Study Tree and then click on the Force tool in the shortcut menu appeared. The Force/Torque PropertyManager appears, see Figure 6.23.

By default, the Vertices, Points button is activated in the Selection rollout of the PropertyManager. As a result, you can select the vertices and points of the beam members to apply the load. On selecting the Joints button, you can select a beam joint to apply the load.

5. Click on the Joints button in the Selection rollout of the PropertyManager to select the beam joint for applying the load.

6. Select the top beam joint. The name of the selected beam joint appears in the field of the Selection rollout in the PropertyManager.

7. Click on the Face, Edge, Plane for Direction field of the Selection rollout in the PropertyManager. Next, expand the FeatureManager Design Tree and then click on the Top Plane as the reference plane to define the direction of force, see Figure 6.24.

8. Make sure that the SI is selected as the unit in the Unit drop-down list of the Units rollout in the PropertyManager.

9. Click on the Normal to Plane button in the Force rollout of the PropertyManager and then enter 14000 as the axial load on the beam, see Figure 6.25.

10. Select the Reverse direction check box in the Force rollout to reverse the direction of force downward, see Figure 6.26.

11. Click on the green tick-mark button in the PropertyManager. The specified compressive axial load is applied on the beam.

1. Right-click on the Mesh option in the Simulation Study Tree and then click on the Create Mesh tool in the shortcut menu appeared. The Mesh Progress window appears and the process of meshing the beam starts. After it is complete, the meshed beam with beam elements, which are represented by hollow cylinders, appear in the graphics area, see Figure 6.27.

1. Click on the Run This Study tool in the Simulation CommandManager . The Beam Buckling Study ( name of the study ) window appears which displays the progress of analysis. When it is complete, the Results folder is added in the Simulation Study Tree with the resultant amplitude of the first mode shape. Also, the first mode shape of the beam appears in the graphics area, see Figure 6.28.

Now, you need to display the buckling factor of safety of the beam.

1. Right-click on the Results folder in the Simulation Study Tree and then click on the List Buckling Factor of Safety tool in the shortcut menu appeared. The List Modes dialog box appears, see Figure 6.29.

The List Modes dialog box displays the number of specified buckling modes and the associated buckling factor of safety of each mode. By default, SOLIDWORKS Simulation, calculates the first buckling factor of safety. It is because, the first buckling load factor is always smaller and for any given load, it occurs first. However, as discussed in the Case Study 1, you can specify multiple buckling modes and the associated buckling factors of safety to be calculated by the program.

The calculated buckling factor of safety is 0.57331 . It means that the design is considered to be failure and the buckling starts when the applied load is equal to 8026.34 N [14000 (applied load) X 0.57331 (buckling load factor)]. Note that you may find difference in the results due to the service packs installed on your system.

Now, you need to calculate the buckling load when the beam can start buckling.

Now, you need to save the results.

1. Click on the Save tool in the Standard toolbar. The model and its results are saved in the location > SOLIDWORKS Simulation > Case Studies > C06 Case Studies > Case Study 2 .

Perform the buckling analysis of a long hollow column shown in Figure 6.30 and determine the buckling load or critical load when the column can start buckling.

The column is clamped at its both ends (top and bottom). You need to apply the Fixed Geometry fixture at the bottom face of the column to represent its clamped connection with the ground, see Figure 6.31. To represent the clamped connection at the top of the column, you need to restrict the radial and circumferential translations of the column at the top so that the column can only translate along its axial direction due to the applied load, see Figure 6.31. The column is subjected to the 1200 Newton compressive axial load on its top, see Figure 6.31. The column is made up of Alloy Steel material.

Hint: To restrict the radial and circumferential translations of the column at the top, you can apply the On Cylindrical Faces fixture and specify the 0 values for the radial and circumferential translations.

In this case study, you will run the buckling analysis of a column which is clamped at its both ends and determine the buckling factor of safety of the beam under the applied compressive load. You also need to calculate the buckling load or critical load based on the minimum buckling factor of safety of the column when it can start buckling.

In this chapter, you have learned about the concept of the buckling analysis. You have also learned about performing the buckling analysis of various case studies. Also, you have learned how to calculate the buckling load or critical load when the structure can start buckling.

• The ________ refers to the larger deformation occurred on a structure due to the compressive axial loads .

• A structure can buckle even if the maximum stress developed in the structure is within the ________ strength of the material.

• The ________ field of the Buckling dialog box is used to specify the number of buckling modes to be calculated by the program.

• The ________ tool is used to display the specified number of buckling modes and the associated buckling factor of safety.

• For any given load, the ________ calculated buckling factor of safety is always smaller than the other buckling load factors.

• The ________ dialog box displays the specified number of buckling modes and the associated buckling factor of safety of each mode.

• If the buckling load factor is less than 1, the design is consider to be ________ and the buckling occurs in the design due to the applied load.

• You can calculate the buckling load or critical load of a structure, when it can starts buckling, by using the ________ buckling factor of safety.