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.

Supported Prestressing/Preloading Loadcases

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

Prestressed/Preloaded Linear Analysis 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).

Prestressing Effect and Prestressed Stiffness Matrix

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

When the prestressing subcase is a linear static one, the prestressing is captured or defined by a geometric stiffness matrix, $K_{σ}$ which is based on the stresses of the preloading static subcase. And this geometric stiffness matrix is augmented with the original stiffness matrix $K$ to form the prestressed stiffness matrix $\bar{K}$ .

$\bar{K} = K + K_{σ}$

The resulting effect could be a weakened or stiffened structure depending on preloading conditions.

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).

Note: The elements CELAS1, CELAS2, CMASS1, CMASS2, CONM1, CONM2, CBUSH, CVISC, CDAMP1, CDAMP2, CGAP, CGAPG, PLOTEL, CWELD, CSEAM, CFAST, and JOINTG do not contribute to the geometric stiffness matrix

$K_{σ}$ .

When the prestressing loadcase is a nonlinear quasi-static subcase, the prestressed stiffness matrix

$\bar{K}$ does not only include the geometric stiffness matrix,

$K_{σ}$ also accounts for the changes of

$K$ due,

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, $\bar{K}$ 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.

For a Prestressed Linear Analysis run, an additional option CNTLCK Subcase Information Entry is available to control the contact open/close status based on the Contact pressure value. The CNTLCK Subcase Information Entry (which references the CNTLCK Bulk Data Entry) should be specified in the Preloading Nonlinear Static Analysis subcase.