Luigi Fenu

TOPOLOGY OPTIMIZATION OF BRIDGES SUPPORTED BY A CONCRETE SHELL

Abstract 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.

Application of Topological Optimization to Bridge Design

AbstractRecently, structural optimization has become an important tool for structural designers, because it allows a better exploitation of material, thus decreasing a structure’s self-weight and saving material costs. Moreover, structural optimization helps the designer to find innovative design solutions and structural forms that not only better exploit material but also give the structure greater aesthetic value from an architectural point of view. In this article, the seismic retrofitting of a bridge originally designed in reinforced concrete is illustrated, showing how lightening the bridge superstructure, rather than reinforcing the already completed foundations and abutments, allowed these latter features to resist greater seismic actions as required in the recent update of the Italian seismic code. Therefore, besides using the steel-concrete composite typology, the bridge superstructure was lightened through structural optimization. After having optimized the thickness of webs and flanges, it was ...

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.

Optimum design of beams surrounded by a Winkler medium

In the present work the analytical approach is used to study the optimization of a beam loaded laterally at the top, not constrained at its ends and surrounded by a Winkler medium. In the literature there are a few examples of studies regarding the optimization of structures constrained both by local constraints and by contact with a medium; in this case the Winkler medium around the beam is the only constraint. The nonlinear system of differential equations governing the problem is solved with an adequate iterative finite difference algorithm. The optimum design of such a beam distributes the great part of the mass near the top; it is seen that the length of beams that are too long is also optimized limiting, in this way, the driving. In the particular case where the moment of inertia is proportional to the area of the cross-section, an analytical solution is also obtained.