could occur.) In this case, it is recommended that you use the subspace eigensolver (BUCOPT,SUBSP)
to achieve a successful solution.
In a linear perturbation buckling analysis, after the solution phase, a stress expansion pass is typically
carried out. A stress expansion must be done along with the buckling analysis in order to use the ap-
propriate material property and to obtain the total sum of elastic strain/stress due to the linear perturb-
ation analysis and the base analysis. A separat e expansion pass (EXPASS command) is not allowed after
the linear perturbation analysis.
9.2.4.4. Second Phase - Harmonic Analysis
As described in Figure 9.4: Flowchart of Linear Perturbation Full Harmonic Analysis (p. 291), the second
phase of a linear perturbation full harmonic analysis consists of the following actions:
- Apply linear perturbation loads to generat e {Fperturbed}. (Note that thermal loads can not be applied
in the second phase of a linear perturbation full harmonic analysis. See Generating and Controlling
Non-mechanical Loads (p. 299) for more information.)- 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. - Regenerate the needed matrices such as mass and damping matrices ([M] and [C]).
- Perform the linear perturbation full harmonic analysis.
User action is needed only for steps (1) and (4) shown above. The program performs steps (2) and (3)
automatically (see Full Harmonic Analysis Based on Linear Perturbation in the Mechanical APDL Theory
Reference for more information.)
Example Input for Linear Perturbation Harmonic Analysis
The following example shows typical command input to accomplish these steps.
HROPT,FULL... (include commands to add or remove lilnear perturbation loads)
HARFRQ,beginning_frequency,end_frequency
NSUB,number_of-frequency_steps
SOLVE
FINISH
In a linear perturbation full harmonic analysis, the strain/stress calculation is done within the frequency
substeps as it is in a standard full harmonic analysis.
9.2.5. Stress Calculations in a Linear Perturbation Analysis
Just as in a standard linear analysis, once the solution eigenvectors or harmonic solution are available,
the stresses or strains of the structure can be calculated.
In general, two choices are available for calculating incremental (perturbation) stresses, depending on
PERTURB command settings and base material properties. By default, the program uses the linear
portion of the nonlinear material constitutive law to recover stresses for all materials, except for hyper-
elasticity. For hyperelasticity, the material property is based on the tangent of the hyperelastic material's
constitutive law at the restart point.
Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationLinear Perturbation Analysis