# Prestressed Linear Analysis

Preloaded or Prestressed Linear Analysis is any type of structural linear analysis performed on a structure under prior loading (also termed preloading or prestressing).

The response of a structure is affected by its initial state and this is in turn affected by the various preloading/prestressing applied to the structure, prior to the analysis of interest. Examples of prestressed linear analysis include analysis of rotorcraft blades under centrifugal preloading, pillar-like structures under compressive preloading, preload arising from the pretensioning of bolts on a structure, etc. OptiStruct can be used to take into account such preloading or prestressing effects.

- Linear static
- Nonlinear quasi-static loadcases (Small and Large Displacement Nonlinear loadcases)

Linear statics, Normal modes, Complex eigenvalue, direct frequency response, modal frequency response, direct transient response, and modal transient response analyses. Preloading for a Component Mode Synthesis (CMSMETH) subcase is also supported.

Specifying preloading in any other unsupported subcase will generate an appropriate user error. Prestressing is specified through the STATSUB(PRELOAD) Case Control card, which refers to the preloading static loadcase ID. Nested preloading is not supported and will generate an appropriate user error (that is: User error will be reported if Subcase C has preloading from Subcase B, which in turn has preloading from Subcase A).

A prestressed stiffness matrix $\overline{K}$, instead of the original stiffness matrix $K$ of the unloaded structure, is used in the prestressed linear analysis to account for the prestressing effect.

- If the preloading is compressive, it typically has a weakening effect on the structure (example: column or pillar under compressive preloading).
- If the preloading is tensile, it typically has a stiffening effect (example: rotorcraft blade under centrifugal preloading).

- Converged contact status
- Instantaneous elastic property
- Spin softening effect from centrifugal load
- Load stiffness effect from pressure and other follower forces

carried over from the prestressing loadcase to the prestressed loadcase. If the prestressing loadcase is an LGDISP quasi-static subcase, $\overline{K}$ is calculated based on the deformed configuration; otherwise, it is calculated based on the initial configuration.

The stiffness calculations in linear analysis preloaded with small displacement NLSTAT analysis can be controlled via PARAM, KSMNL4PL.

## Prestressed Linear Analysis Types

Below are the different prestressed linear analysis types.

### Static Analysis

While linear static subcases can have prestressing, nonlinear static subcases under prestressing are not supported.

### Normal Modes Analysis

Prestressed eigenvalue analysis is currently supported by AMSES, AMLS and the Lanczos Method. However, if the specified preload is greater than the first critical buckling load, an appropriate error will be reported for AMSES/AMLS runs.

### Complex Eigenvalue Analysis

In addition to Prestressed Complex Eigenvalue Analysis implementation, Brake Squeal Analysis can be performed via the STATSUB(BRAKE) command, wherein the contribution of friction to the stiffness matrix is automatically included. For further information, refer to Brake Squeal Analysis in the User Guide.

### Direct Frequency Response Analysis

### Modal Frequency Response Analysis

### Direct Transient Response Analysis

### Modal Transient Response Analysis

### Component Mode Synthesis (CMSMETH) Subcase

Prestressed Component Mode Synthesis (CMS) uses ($$\overline{K}$$) as the stiffness matrix, with other aspects such as the mass and damping matrices remaining unchanged in order to calculate the static and normal modes for both flexible body generation (as an input to multibody dynamics) and direct matrix input generation (for external superelements). The primary effect of a preloaded/prestressed CMS analysis will be a frequency shift in the results.

## Results

All results that are supported for regular structural linear analyses are also available in the corresponding prestressed linear analyses.

It is important to note that, while the prestressed linear analysis includes the effects of preloading as a weakening or a stiffening of the structure, the results from the prestressed analysis do not include the preloading results. For example, the displacements from prestressed linear static analysis do not include the preloading displacements. In order to get the overall deflection/stresses of the structure, the displacements/stresses from the prestressed linear analyses have to be carefully superposed with the preloading displacements/stresses while post-processing. Particularly, while post-processing complex results from prestressed direct FRF, the correct approach would be to first obtain the complex results for a certain phase and then superpose the appropriate preloading result. Any other superposing approach would lead to incorrect results.