Prestressed Structures
You can analyze eigenfrequency, frequency domain, or time-dependent problems where the dynamic properties of the structure are affected by a preload, such as a tensioned string.
Usually, a study of a prestressed problem includes using two study steps. The first step is a Stationary step in which the static preload is applied. The preload step can be computed with or without taking geometric nonlinearity into account. In the second study step, where you compute the eigenfrequency or the frequency response, it is necessary to take geometric nonlinearity into account. Even if the displacements and strains are small, this is what gives the prestress contribution to the equations.
There are three predefined study sequences for prestressed dynamic analysis:
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Eigenfrequency, Prestressed
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Frequency Domain, Prestressed
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Frequency Domain, Prestressed, Modal
The prestressed study types assume that the loading causes small perturbations around the prestressed state.
In the predefined study sequences, the Include geometric nonlinearity checkbox is selected by default also in the stationary prestress study step.
In many cases, a geometrically linear assumption is sufficient for this step. If no other nonlinearities are present in the prestress step, you can improve performance by instead using a geometrically linear formulation, thus avoiding unnecessary iterations.
To understand which option to use, it is important to understand how the two study steps are linked. It is the displacement field of the first study step that is used for computing the stresses including stress stiffening effects in the second study step. Thus, it does not directly matter whether the stresses in the first study step are right or wrong. The only thing that matters is that when you switch from a geometrically linear to a geometrically nonlinear formulation, the stresses that you get with the nonlinear formulation are correct enough, using the given displacement field.
In a general nonlinear analysis, like a Stationary or Time Dependent study step, the full combined effect of the prestress and other loads will automatically be included.
The same principles apply also to a linear buckling analysis, except that both study steps should be geometrically linear. The nonlinear contribution is included in the formulation of the buckling eigenvalue itself.
Follower Loads
Loads that change orientation with deformation, such as a pressure, actually contribute not only to the load but also to the stiffness. This is a physical effect and not just a numerical artifact. Whether such loads are included or not in an Eigenfrequency study step will affect the computed eigenfrequencies. If you for some reason do not want this effect, you must suppress the load in the Physics and Variables section of the Eigenfrequency node.
If you use a local coordinate system for describing a load, you must, in case of geometric nonlinearity, pay attention to whether that coordinate system has constant axis orientations or not. As an example, the default boundary system has Frame set to Deformed Configuration, so that a load represented in that system will behave as a follower load. Change to Reference Configuration if the load should act in fixed directions.
In more general terms, any feature in which there is a dependency on the choice of frame (material or spatial) can potentially affect the outcome of a prestressed analysis.
Contact and Prestressed Analysis
If a contact is included in the prestress load case, you can perform a subsequent eigenfrequency or frequency-domain analysis in which the linearization will be made around the computed contact state. The connection between the two boundaries is elastic, using the penalty factor as stiffness, both for the penalty method and the augmented Lagrangian method. If the augmented Lagrangian method is used for the contact modeling, then the penalty factor must be constant and not dependent on the iteration number.
The contact state is considered as fixed, so there is no harmonic perturbation in contact quantities, such as the contact pressure.
The gap distance in a contact analysis is computed from the coordinates of the contacting boundaries in the spatial frame. The spatial frame is defined by the displacements in the preload step and is not affected by the displacements in a subsequent perturbation step.
Inelastic Stresses and Strains
When inelastic stresses and strains are part of the problem description, you need to make some extra considerations. Such contributions are formally part of the constitutive model but generate load vector contributions.
There are three Preset study types which can be used to set up these two study steps: Eigenfrequency, Prestressed; Frequency Domain, Prestressed; and Linear Buckling.
If you want to explicitly prescribe the stress field for a prestressed analysis rather than solving for it, you should not use the two study step procedure. In such a case, prescribe the stress field using an Initial Stress and Strain, External Stress, or External Strain node. Then add a separate Eigenfrequency or Frequency Domain study and select Include Geometric Nonlinearity in the settings for the study step.
Eigenfrequency, Prestressed, Frequency Domain, Prestressed, and Linear Buckling in the COMSOL Multiphysics Reference Manual
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For an example of a general prestressed eigenfrequency analysis see Bracket — Eigenfrequency Analysis: Application Library path Structural_Mechanics_Module/Tutorials/bracket_eigenfrequency.
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For an example of an analysis where the stress state is explicitly prescribed, see Vibrating Membrane: Application Library path Structural_Mechanics_Module/Verification_Examples/vibrating_membrane.