Topology optimization with eigenfrequency of concrete shell bridge

Shell supported bridges whose deck is supported by a shell structure are special spatial bridge structures shaped by means of a form-finding algorithm. In order to achieve mainly membrane stresses and avoid bending effects, Zordan et al.(2010) carried out a finite element topological optimization procedure by means of the SIMP (Solid Isotropic Material with Penalization) method, with the goal of minimizing compliance^]. Meanwhile, although eigenfrequency optimization applied to shell structures is infrequent, the topological optimization procedure can be also used to maximize the fundamental natural frequency of shell structures, and is also effective in reducing the arising of tensile stresses. In this paper, starting from a shell surface obtained through a form-finding process and that supports the deck of a footbridge, the finite element topological optimization with eigenfrequency was carried out by using the SIMP method to both maximize the fundamental natural eigenfrequency and minimize of a certain percentage the weight (volume) of the shell itself. Topological optimization through the SIMP method first identified the shell regions with lower pseudo densities, while the geometry of the shell was updated by eliminating the inefficient material in these regions. Although maximizing the fundamental eigenfrequency with topological optimization is not so effective compared to other slender structures because of the intrinsic stiffness of the concrete shell structure itself, the area of shell regions where tensile stresses arose was however clearly minimized.