A bi-level heuristic for skew reinforcement in concrete shells subjected to different loading conditions

In structural design, structures are often modeled using the finite elements method (FEM). One of the most common element type is the shell, which is used to model surfaces in three dimensional space as far as the surface thickness is smaller than the other two dimensions. Designers are generally interested in providing a solution that respects all the problem constraints and guarantees structural safety [1], without trying to further improve it as optimization is not trivial even if it could yield a huge benefit both from the economic and the construction point of view. Additionally, saving materials is one of the fundamental criteria for the sustainable approach to the design. In this paper we address the Skew Reinforcement Design in Reinforced Concrete Two Dimensional Elements (SRD2D) under multiple loading conditions. It consists of determining the minimum reinforcement required to respect all the constraints given by the geometric properties and the internal actions working on it, for all the loading conditions that may occur, i.e. for different combinations of internal actions acting on the element. We present a heuristic framework that guides a Genetic Algorithm. Computational results show the efficacy and the effectiveness of the method