Mechanical APDL Structural Analysis Guide

In a linear perturbation modal analysis, after the solution phase, a stress expansion pass is typically
carried out. A stress expansion must be done along with the modal analysis in order to use the appro-
priate material property and to obtain the total sum of elastic strain/stress due to the linear perturbation
analysis and the base analysis. A separat e expansion pass (EXPASS command) is not allowed after the
linear perturbation analysis.

9.2.4.3. Second Phase - Eigenvalue Buckling Analysis

As described in Figure 9.3: Flowchart of Linear Perturbation Eigenvalue Buckling Analysis (p. 290), the
second phase of a linear perturbation eigenvalue buckling analysis consists of the following actions:

1. Apply linear perturbation loads to generat e {Fperturbed}. (Note that thermal loads can be applied in

the second phase of a linear perturbation eigenvalue buckling analysis. See Generating and Controlling

Non-mechanical Loads (p. 299) for more information.)

2. Solve for {Uperturbed} from i

T

 { Perturbed}={Perturbed}. This step is executed automatically and

internally by the program.

3. Generate the linear stress stiffness matrix s

 L





using {Uperturbed}. This step is executed automatically

and internally by the program.

4. If the base analysis included NLGEOM,ON, update the nodal coordinates by using the total displace-
   ment from the base analysis (similar to the UPCOORD command, but executed automatically and
   internally in this phase). From this point on, the deformed mesh is used for calculating perturbation
   loads and for postprocessing results from the linear perturbation analysis.


5. Perform the linear perturbation eigenvalue buckling analysis to solve

j j 



 { }φ −λi { }φj = ,

where φj are the eigenvectors and λj are the eigenvalues.

In a linear perturbation eigenvalue buckling analysis, the perturbation load {Fperturbed} does not include

external loads introduced by contact gaps or penetrations, even if these loads were applied in the prior
static or transient load steps.

User action is needed only for steps (1) and (5) shown above. The program performs steps (2), (3), and
(4) automatically (see Eigenvalue Buckling Analysis Based on Linear Perturbation in the Mechanical APDL
Theory Reference).

The following example shows typical command input to accomplish these steps.

Example Input for Linear Perturbation Buckling Analysis

BUCOPT,eigensolver,number_of_modes,

... (include commands to add or remove linear perturbation loads)
MXPAND,number_of_modes,
SOLVE
FINISH

Generally, the Block Lanczos eigensolver (BUCOPT,LANB) performs well for perturbed eigenvalue
buckling analyses. However, when the tangent stiffness matrix becomes indefinite, the Block Lanczos
eigensolver could fail to produce an eigensolution due to the mathematical limitation of this solver
(refer to Eigenvalue Buckling Analysis Based on Linear Perturbation for more information on when this

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General Procedure for Linear Perturbation Analysis