Convex polytopic models for the static response of structures with uncertain-but-bounded parameters

This chapter proposes a novel convex polytopic model for the static response of structures with uncertain-but-bounded parameters, and its vertex solution theorem to predict the exact bounds of the static displacements. It presents the convex polytopic model for the static response of structures with uncertain-but-bounded parameters. The chapter provides the vertex solution theorem of the convex polytopic model for exact bounds of the structural static displacements. It also provides three numerical examples to illustrate the effectiveness of the vertex solution theorem based on the convex polytopic model, including a two-step bar, a ten-bar truss and a plane frame. The chapter demonstrates the validity of the vertex solution theorem of convex polytopic model, by calculating the upper and lower bounds of the static displacements of the ten-bar truss. The proposed method can play a significant role in static displacement bound estimation and become a powerful tool in static response analysis with uncertainties.