In many engineering applications, the linear behavior of a structure based on a prior linear or nonlinear preloaded status is of interest. The linear perturbation analysis is designed to solve a linear problem from this preloaded stage. In the nonlinear analysis, the Newton-Raphson procedure is typically used (see Nonlinear Structural Analysis). The tangent matrix from the Newton-Raphson analysis can be used in the linear perturbation analysis in order to obtain the preloaded solution, since the linear stiffness matrix without preloading would not give an accurate solution.
Generally speaking, the linear perturbation analysis can be any analysis type. However, the program currently supports only linear perturbation static analysis, linear perturbation modal analysis, linear perturbation buckling analysis, linear perturbation harmonic (full, frequency-sweep VT, or Krylov) analysis, and linear perturbation substructure analysis.
Most current-technology elements are supported in a linear perturbation analysis. See Elements Under Linear Perturbation in the Element Reference.
The following linear perturbation topics are available:
- 9.1. Understanding Linear Perturbation
- 9.2. General Procedure for Linear Perturbation Analysis
- 9.3. Considerations for Load Generation and Controls
- 9.4. Considerations for Perturbed Stiffness Matrix Generation
- 9.5. Considerations for Rotating Structures
- 9.6. Example Inputs for Linear Perturbation Analysis
- 9.7. Where to Find Other Examples