COMSOL 6.4 - Bracket — Transient Analysis

Transient analyses provide the time-domain response of a structure subjected to time-dependent loads. A transient analysis can be important when the time scale of the load is such that inertial or damping effects have a significant influence on the behavior of the structure.

In this example, you learn how to add damping properties to the material, define external loads varying with time, set up time-stepping data for the study, and generate animations.

It is recommended you review the Introduction to the Structural Mechanics Module, which includes background information and discusses the bracket_basic.mph models relevant to this example.

Model Definition

This model is an extension of the example described in the section “The Fundamentals: A Static Linear Analysis” in the Introduction to the Structural Mechanics Module.

The model geometry is represented in Figure 1.

Figure 1: Bracket geometry.

A rigid body, on which the time-varying load is applied, is assumed to be connected to the arms of the bracket. This body is modeled using a rigid connector. The following loads are applied:

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In the x direction, a 400 N load applied between 4 and 4.5 ms

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In the y direction, a 500 N force with300 Hz sinusoidal time dependence

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In the z direction, a constant load −100 N

Rayleigh damping is chosen here with relative damping set to 0.01 and 0.02 at the frequencies 216 Hz and 1515 Hz, respectively. The resulting damping ratio curve is shown in Figure 2.

Figure 2: The damping ratio curve.

Results and Discussion

Figure 3 shows the rigid connector’s displacements at the center of rotation versus time.

Figure 3: Displacement of the pin center of rotation versus time.

Figure 4: von Mises stress distribution in the bracket (from top to bottom, t = 7 ms, 8 ms, 9 ms and 10 ms).

Notes About the COMSOL Implementation

To accurately model the physical problem, you need to apply damping in a dynamic analysis. In COMSOL you have the possibility to add damping of several types, for example loss factor damping, viscous damping, or Rayleigh damping. Damping is also inherent in some material models, like viscoelasticity.

To describe time-dependent boundary conditions you can enter expressions using the built-in time variable, t.

To improve accuracy, the scaling of the displacement variables can be changed to correspond to the expected deformations. Manual scaling is the default for the displacement variables. The default manual scaling used for the structural displacement is 1% of the geometry size. In this example, the size of the geometry is about 200 mm, so the assumed displacement scale is 2 mm. In this case, the expected deformations are in the order of 0.1 mm. The manual scaling factor should thus be changed to 10-4.

Because of the constant load in the z direction, the initial zero displacement assumption is not consistent with the boundary conditions. This singularity at initial time would induce high frequency dynamics requiring a small time step. To avoid issues at the initial time, it is recommended to use a smooth step function to ramp up the load. Another alternative would be to solve a stationary study first with only the static load, and then use the results from that study as initial conditions for the time-dependent analysis.

Two action buttons are provided in the section in order to visualize the damping ratio with respect to frequency. The first button shows a dynamic preview plot of the damping ratio, while the second button generates a plot in the node.

Structural_Mechanics_Module/Tutorials/bracket_transient

Modeling Instructions

Application Libraries

From the menu, choose .

In the window, select > > in the tree.

Click

Solid Mechanics (solid)

Linear Elastic Material 1

In the window, expand the > node, then click .

Damping 1

In the toolbar, click

and choose .

In this example, you will use Rayleigh damping defined using damping ratios.

In the window for , locate the section.

From the list, choose .

In the f1 text field, type 200.

In the ζ1 text field, type 1e-2.

In the f2 text field, type 1500.

In the ζ2 text field, type 2e-2.

In order to visualize the damping ratio curve, create the plot through an action button from the section.

Click in the upper-right corner of the section. From the menu, choose .

Results

Damping Ratio Plot

In the window, under click .

In the toolbar, click

Global Definitions

Step 1 (step1)

In the toolbar, click

and choose > .

In the window for , locate the section.

In the text field, type 1[ms].

Click to expand the section. In the text field, type 2[ms].

Rectangle 1 (rect1)

In the toolbar, click

and choose > .

In the window for , locate the section.

In the text field, type 4[ms].

In the text field, type 4.5[ms].

Click to expand the section. Clear the checkbox.

Parameters 1

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
t	0[s]	0 s	Time
F_x	400[N]*rect1(t)	0 N	Applied force, x-component
F_y	500[N]sin(2pi300[Hz]t)	0 N	Applied force, y-component
F_z	-100[N]*step1(t)	-0 N	Applied force, z-component

This way of adding time dependent functions as parameters is possible, since they can be evaluated when t is also a parameter. By doing so, it is easy to verify that the loads in all directions are zero at the initial time. This is consistent with the initial conditions.

Solid Mechanics (solid)

To represent the pin between the arms of the bracket use a rigid connector to which a load is applied.

Rigid Connector 1

In the toolbar, click