Topology optimization of bridges supported by a concrete shell

A shell-supported footbridge was designed by shaping an anticlastic membrane in compression between deck and foundations. Since it would be subject to biaxial compression, it was appropriate to be made of concrete because concrete strength could be exploited and crack propagation prevented. With reference to Musmeci's work, a form-finding algorithm shaped the shell as a tension structure with same loads, restraint reactions and internal normal forces, but with the opposite sign. Using a finite element (FE) model of the shell, unwished bending moments (and therefore tensile stresses) were, however, found, because of second order displacements and (contrary to a tension structure) because of the bending stiffness of the reinforced concrete (RC) shell. Tensile stresses were progressively eliminated by removing material from the shell regions where unwished bending moments occurred. For this purpose, topology optimization with the Solid Isotropic Material with Penalization (SIMP) method was used, and different shell structures with cavities for different values of given volume reduction were obtained. Appropriate indexes for structural response were defined, and an optimization index was finally used to identify the most suitable pattern of cavities along the shell.