This analysis solves for the transient solution of the displacements and velocities as functions of time. The material properties, forces, and boundary conditions can vary in time.
The purpose of this analysis is to find the transient response from a harmonic load during the first five periods. The excitation frequency is 500 Hz, which is between the first and second eigenfrequencies found in the eigenfrequency analysis.
This load is applied on the face indicated in Figure 2. The expression for the load can be written as
(2) where t denotes the time in seconds.
Results and Discussion
Because the loading is harmonic, the expected solution will consist of an initial transient, and after long time the response will be a stationary harmonic solution with its amplitude controlled by the damping of the system.
Fx = 1.5⋅[1+sin(2π 500 t π 2⋅ ⋅ – ⁄ )] MPa
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The following plot shows the x-displacement at a point on the loaded face:
Figure 7: x-displacement at a point on the loaded face.
The figure below shows the von Mises stress in the bracket at 0.0036 s. The maximum value is 252 MPa.
Figure 8: von Mises stress at t = 3.6 ms.
Solved with COMSOL Multiphysics 4.2a
Notes About the COMSOL Implementation
In order to get a good accuracy, you should set the absolute tolerance value to a reasonable value smaller than the actual expected displacements. The solution is always performed in the selected base unit system, so tolerances should in this case be expressed in m.
When a harmonic load is used, the time step can sometimes oscillate in an inefficient manner, causing longer solution times. This can be avoided by using the more restrictive time stepping obtained by selecting the check box for Time step increase delay.
For more information on the settings for the time-dependent solver, see Time Dependent in the COMSOL Multiphysics Reference Guide.
Modeling Instructions
If you are working from the beginning of this example, ignore the next four instructions. If you are starting from the short model version described in Static and Eigenfrequency Analyses of an Elbow Bracket, load that model as described here:
1 From the View menu, choose Model Library. 2 Go to the Model Library window.
3 In the Model Library tree, select Structural Mechanics Module>Tutorial Models>elbow bracket brief.
4 Click Open.
M O D E L W I Z A R D
1 In the Model Builder window, right-click elbow_bracket_brief.mph and choose Add Study.
2 Go to the Model Wizard window.
3 Find the Studies subsection. In the tree, select Preset Studies>Time Dependent. 4 Click Finish.
S T U D Y 4
Solving for five periods with an excitation frequency of 500 Hz means solving for 10 ms. Save the solution every 0.2 ms.
Step 1: Time Dependent
1 In the Model Builder window, click Study 4>Step 1: Time Dependent.
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2 Go to the Settings window for Time Dependent.
3 Locate the Study Settings section. In the Times edit field, type range(0,2e-4,10e-3).
4 In the Model Builder window, right-click Study 4 and choose Rename.
5 Go to the Rename Study dialog box and type Study 4 (Time-Dependent) in the New name edit field.
6 Click OK.
7 Right-click Study 4 and choose Show Default Solver. S T U D Y 4 ( T I M E - D E P E N D E N T )
Solver 4
1 In the Model Builder window, expand the Study 4 (Time-Dependent)>Solver Configurations node.
2 Right-click Study 4 (Time-Dependent)>Solver Configurations>Solver 4 and choose Rename.
3 Go to the Rename Solver dialog box and type Time-Dependent Sequence in the New name edit field.
4 Click OK.
Time-Dependent Sequence
1 In the Model Builder window, expand the Study 4 (Time-Dependent)>Solver Configurations>Time-Dependent Sequence node, then click Time-Dependent Solver 1. 2 Go to the Settings window for Time-Dependent Solver.
3 Click to expand the Absolute Tolerance section.
4 In the Tolerance edit field, type 1e-5. 5 Click to expand the Time Stepping section.
6 Select the Time step increase delay check box. Keep the default value of 15.
This setting instructs the solver not to increase the time step until 15 consecutive steps have been successful.
7 In the Amplification for high frequency edit field, type 0.95.
By raising this value from its default value of 0.75 you reduce the damping of high frequencies.
You can reduce the file size significantly by not storing time derivatives when not needed.
Solved with COMSOL Multiphysics 4.2a
8 Click to expand the Output section.
9 Clear the Store time-derivatives check box.
R E S U L T S
Before computing the solution, prepare a plot for displaying the results during the solution process.
Data Sets
1 In the Model Builder window, right-click Results>Data Sets>Solution 4 and choose Rename.
2 Go to the Rename Solution dialog box and type Time-Dependent Solution in the New name edit field.
3 Click OK. 1D Plot Group 6
1 Right-click Results and choose 1D Plot Group. 2 Go to the Settings window for 1D Plot Group.
3 Locate the Data section. From the Data set list, choose Time-Dependent Solution. 4 Right-click Results>1D Plot Group 6 and choose Point Graph.
5 Select Point 30 only.
6 Go to the Settings window for Point Graph.
7 In the upper-right corner of the y-Axis Data section, click Replace Expression. 8 From the menu, choose Solid Mechanics>Displacement>Displacement field
(Material)>Displacement field, X component (u).
9 Locate the y-Axis Data section. From the Unit list, choose mm. 10Select the Description check box.
11In the associated edit field, type X displacement on loaded face. 12In the Model Builder window, right-click 1D Plot Group 6 and choose Rename. 13Go to the Rename 1D Plot Group dialog box and type Time-Dependent
Displacement Graphs in the New name edit field.
14Click OK.
S T U D Y 4 ( T I M E - D E P E N D E N T )
Step 1: Time Dependent
1 In the Model Builder window, click Study 4 (Time-Dependent)>Step 1: Time Dependent.
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2 Go to the Settings window for Time Dependent.
3 Click to expand the Results While Solving section.
4 Select the Plot check box.
5 From the Plot group list, choose Time-Dependent Displacement Graphs.
S O L I D M E C H A N I C S
A new load is needed for this study. You could just change the existing one, but when you have multiple studies it is better to have individual load features and disable the ones not currently used.
Boundary Load 1
1 In the Model Builder window, right-click Boundary Load 1 and choose Rename. 2 Go to the Rename Boundary Load dialog box and type Static Load in the New name
edit field.
3 Click OK.
4 Right-click Boundary Load 1 and choose Disable. Boundary Load 2
1 Right-click Solid Mechanics and choose Boundary Load.
2 In the Model Builder window, right-click Boundary Load 2 and choose Rename. 3 Go to the Rename Boundary Load dialog box and type Time-Dependent Load in the
New name edit field.
4 Click OK.
5 Select Boundary 29 only.
6 Go to the Settings window for Boundary Load.
7 Locate the Force section. Specify the FA vector as
S T U D Y 4 ( T I M E - D E P E N D E N T )
In the Model Builder window, right-click Study 4 (Time-Dependent) and choose Compute. 1.5[MPa]*(1+sin(2*pi*500[Hz]*t-pi/2)) X
0 Y
0 Z
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R E S U L T S
Time-Dependent Displacement Graphs
Compare the result for the x-displacement with the graph shown in Figure 7.
3D Plot Group 7
1 In the Model Builder window, right-click Results and choose 3D Plot Group. 2 Right-click Results>3D Plot Group 7 and choose Surface.
3 Go to the Settings window for Surface.
4 In the upper-right corner of the Expression section, click Replace Expression. 5 From the menu, choose Solid Mechanics>Stress>von Mises stress (solid.mises). 6 Right-click Surface 1 and choose Deformation.
7 In the Model Builder window, click 3D Plot Group 7. 8 Go to the Settings window for 3D Plot Group.
9 Locate the Data section. From the Data set list, choose Time-Dependent Solution. 10From the Time list, choose 0.0036.
11Click the Plot button.
Before generating a movie of the solution, you need to fix the scale factor for the deformation; otherwise this factor is automatically adjusted for each movie frame in such a way that the elbow does not move in the Graphics window.
12In the Model Builder window, click Surface 1>Deformation 1. 13Go to the Settings window for Deformation.
14Locate the Scale section. Select the Scale factor check box.
15In the Model Builder window, right-click 3D Plot Group 7 and choose Rename. 16Go to the Rename 3D Plot Group dialog box and type Time-Dependent Stress
Contour in the New name edit field.
17Click OK.
18Right-click 3D Plot Group 7 and choose Player.