**Buckling with Inertia Relief**

In OptiStruct, starting from version **2023.1**, buckling analysis referring to an inertia-relieved static subcase under STATSUB(BUCKLING) will result in an error message reported to the user (Error message 311). This is because under inertia relief, while the stress states are correct in the model, the SUPORT dofs influence the buckling eigenvalues and eigenvectors. Therefore, OS does not allow buckling to refer to inertia-relieved static subcase, by default.

There is a parameter which will allow buckling subcase to refer to an inertia-relieved static subcase:

PARAM, INRELBCK, 1.

With this parameter set to 1, the buckling eigenvalue analysis will use the SUPORT dofs from inertia relief as constraints. For param, inrel, -1, this implies that the buckling analysis will constrain the user specified SUPORT dofs. For param, inrel, -2, if SUPORT dofs are internally generated during the static analysis, those internally generated SUPORT dofs will be constrained during the buckling analysis. Alternatively, if param, inrel, -2 enforces inertia relief through internally generated orthonormality constraints (MPCs), SUPORT dofs will be generated based on the inertia-relieved displacement field from the static analysis and these SUPORT dofs will be constrained during the buckling analysis.

**Figure 1: Wing Model**

The wing model of **Figure 1** has been used to calculate buckling load factors with inertia relief approach. Parameters used for the calculation are:

PARAM,INRELBCK,1

PARAM,INREL,-2

PARAM,PRINFACC,1

The model has 3 loadcases: a pressure distribution, a tip force and the combination of the previous loads. Rigid body forces and accelerations for the 6 rigid body modes have been requested for output at geometric center of the model.

Rigid body forces can be checked to match applied loads. For Loadcase 2, tip force is acting on y direction with a total magnitude of 4000N.

Rigid forces balance is equal to:

**Figure 2: Load balance for LC2**

Buckling factors for the 3 loadcases are:

· LC1(pressure) = 85.1;

· LC2(tip force) = 14.6;

· LC3(tip force+pressure) = 14.6.

First buckling modes for the 3 loadcases are shown in **Figure 3**.

**Figure 3: 1st buckling modes**