Unified form for static displacement, dynamic response and natural frequency analysis based on convex models

Unified form of analysis for the static displacement, the dynamic response and the natural frequency of structures with uncertain-but-bounded parameters based on convex models is presented. The probabilistic model for them is also given, where the uniform distribution is adopted for the uncertain parameters. The mean values and the standard deviations of the uncertain parameters are derived from the ellipsoid so that the relationship between convex models and probabilistic model is established. Numerical examples are used to illustrate the validity of the presented methods.