The linear perturbation analysis can be considered an iteration on top of a base (or prior) linear or nonlinear analysis. During the linear perturbation process, all of the linear or nonlinear effects from the base analysis are taken into account and are “frozen” so that the perturbation loads can generate structural results (such as deformation, stresses, and strains) linearly by using the "frozen" solution matrices and material properties. The linear or nonlinear effects from the base analysis are also carried over to the stress expansion pass, if applicable. However, for any downstream analysis, such as a linear dynamic analysis, only linear effects are accounted for.
If the linear or nonlinear effects from the base analysis are not of interest, there is no need to perform a linear perturbation analysis. A simple one-step linear or nonlinear analysis can serve that purpose.
To perform a linear perturbation analysis:
The total tangent stiffness matrix from the prior solution (the base analysis) must be obtained for the current linear perturbation analysis. This matrix is regenerated in the first phase of the linear perturbation procedure.
The total perturbation load must be established. This load vector is calculated in the second phase of the linear perturbation procedure.