Linear Buckling
The Linear Buckling () study and study step are used for estimating the critical load at which a structure becomes unstable.
The Linear Buckling study consists of two study steps: a Stationary study step for applying an external load followed by a Linear Buckling study step. In the second study step, an eigenvalue solver is used to compute the buckling modes and the associated critical load factors.
A Linear Buckling analysis includes the stiffening effects from stresses coming from nonlinear strain terms. The stiffness coming from stresses and material defines an eigenvalue problem in which the eigenvalue is a load factor that, when multiplied with the actual load, gives the critical load in a linear context.
Another way to calculate the critical load is to include large deformation effects and increase the load until the solver fails because the load has reached its critical value.
The Linear Buckling study is available for the Solid Mechanics interfaces using the Structural Mechanics Module or the MEMS Module. It is also available with Shell, Plate, and Truss interfaces when using the Structural Mechanics Module.
Study Settings
If desired, select the Include geometric nonlinearity check box.
Use the Desired number of buckling modes field to specify the number of buckling modes you want the eigenvalue solver to return (by first selecting the associated check box).
Use the settings under Values of linearization point to specify a linearization point.
From the Settings list, choose Physics controlled (the default) to use linearization point settings controlled by the physics interfaces. Choose User defined to specify the linearization point using the Method list. Select:
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 Initial expression to use the expressions specified on the Initial Values nodes under a specific physics interface as a linearization point.
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 Solution to use a solution as a linearization point.
Use the Study list to specify which solution to use from the available studies. Select:
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 Zero solution to use a linearization point that is identically equal to zero.
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Any other available solution to use it as a linearization point. It can be the current solution in the sequence, or a solution from another sequence, or a solution that was stored with the Solution Store node. You select a stored solution by changing Use to the name of the stored solution. Choose a solution using the Selection list (see Values of Dependent Variables under Common Study Step Settings).
Under Live loads solution, you can specify the solution to use for the live loads. In certain studies, only some of the loads should be multiplied by the load factor λ in a linear buckling analysis. Other loads, like self-weight, should be treated as constant loads. These two types of loads are commonly called live loads and dead loads, respectively.
From the Settings list, choose Same as linearization point (the default) to use the same settings as for the linearization point above. Choose User controlled to use a separate solution for the live loads. See the settings for the linearization point for the user-controlled settings.
Study Extensions
This section contains some optional extensions of the study, such as auxiliary sweeps (see Common Study Step Settings). Adding an auxiliary parametric sweep adds an Eigenvalue Parametric attribute node to the Eigenvalue Solver.
Distribute Parametric Solver
If you are running an auxiliary sweep and want to distribute it by sending one parameter value to each compute node, select the Distribute parametric solver check box. To enable this option, click the Show More Options button () and select Batch and Cluster in the Show More Options dialog box.
For more information about performing a linear buckling analysis, see Linearized Buckling Analysis in the Structural Mechanics User’s Guide.
The Include geometric nonlinearity check box should have the same selection in booth study steps in a Linear Buckling Study.
The default to use a geometrically linear analysis. There are some cases when the preload step requires a geometrically nonlinear analysis, and in that case you must use it also in the Linear Buckling study step.
The Physics and Variables Selection, Values of Dependent Variables, Mesh Selection, Adaptation and Error Estimates, and Geometric Entity Selection for Adaptation sections and the Include geometric nonlinearity check box are described in Common Study Step Settings. There is also detailed information in the Physics and Variables Selection and Values of Dependent Variables sections.
With the Structural Mechanics Module: Bracket — Linear Buckling Analysis, Application Library path Structural_Mechanics_Module/Tutorials/bracket_linear_buckling.