Optimization indexes to identify the optimal design solution of shell-supported bridges

As a structural optimization technique, topology optimization is an important tool for helping designers to determine the most suitable shape of a structure. With this powerful tool, designers can define families of candidate solutions by modifying the input volume reduction (VR) ratio, reducing the structural weight as much as possible. However, finding the best compromise between material savings and structural performance among these candidate solutions is a critical issue for designers. To deal with this issue, an optimization index (OI) is presented in this paper. It provides a mathematical procedure that highlights the best choice among several candidate solutions obtained by the optimization procedure. The index was originally defined in a previous study on the structural optimization of composite steel-concrete bridges. In this paper, a generalized version of the original optimization index is introduced and used to investigate a particular aspect related to concrete shell-supported bridges. Starting from three shell-supported footbridges, the shapes of which are the final result of form-finding optimization procedures, different starting models are defined, and each is characterized by different edge-stiffening conditions. Despite using an anticlastic shell shape, unavoidable tensile stresses occur because of the thickness of the shell, variations in the material, the loading of the deck, and other factors. For each starting model, a finite-element topological optimization conducted with the solid isotropic material with penalization (SIMP) method is performed to minimize the weight (i.e., volume) of the shell by a certain percentage. According to the results obtained from topology optimization, the proposed generalized optimization index (OI∗) analytical formulation is discussed in detail, and its effectiveness is validated.