This structure is composed of both steel bars and cables. The existence of cables is required for the deployment of the structure from a fully-retracted state to a fully-deployed state. After the deployment, the cables are given pres-tressing forces to create a state of self-stressed equilibrium the makes the structure stable and has sufficient stiffness to sustain different loadings.
If you have an initial static case with geometric nonlinearity included and the modal analysis uses its stiffness (and not the pure linear) it could be adequate.
There are methods available to estimate inelastic effects using a linear response spectrum analysis. The keys are to adopt (1) a substitute structure based on secant stiffness to maximum displacement, (2) an appropriate model for effective system damping and (3) an appropriate model for response modification due to the increased damping. This is an iterative procedure in that you need to know the maximum displacement in order to calculate the secant stiffness, but you need to know the secant stiffness in order to run the analysis and find the maximum displacement. The attached link may help if you decide to go this route. However, given the description, I tend to agree with the conclusion of Carlos above - a nonlinear response history analysis using properly selected and modified ground motions is the safe route here.
Article Inelastic Displacement Spectra for Bridges Using the Substit...
Using the equivalent stiffness as mentioned by Stoyan Andreev and Carlos Méndez-Esteban the response spectrum analysis can be performed but the results are not as accurate as those of time history analysis based on the complete geometric nonlinear analysis. In a complete geometric nonlinear procedure, I will recommend only the time history analysis based on my current research results ( "Dynamic analysis of submerged floating tunnel supported by 3D cables", This is my ongoing work which is almost done).
I agree that inelastic response history analysis is the "most accurate", provided that the ground motions are properly selected and scaled or spectrally matched to the correct target response spectrum. Without proper ground motion selection and modification, the effort will be wasted. Be careful on that point. Other critical issues for inelastic analysis include damping (tangent stiffness based versus initial stiffness based), selection of the proper element type for modeling the components, and appropriate material models.
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