Budapesti Műszaki és Gazdaságtudományi EgyetemÉpítőmérnöki Kar - építőmérnök képzés 1782 óta

Structural optimization is a powerful design tool to sketch lightweight components searching the design domain for the layout of material that minimizes a prescribed objective function, given a set of constraints. Size, shape, and topology optimization are extensively exploited in many branches of engineering, including applications in civil engineering and construction industry [1]. In these fields, techniques of large-scale additive manufacturing are well-suited to bring optimal layouts from concept to reality, since they considerably reduce restrictions imposed by traditional manufacturing techniques. However, peculiar features of the printing process should be accounted for, as well as constraints on the material strength and the prescribed structural performances [2].

In this research attention will be directed to the optimization of reticulated shells and spatial trusses, combining the force density method along with techniques of sequential convex programming. The former is a viable approach to handle the equilibrium of the loaded nodes of any spatial networks in terms of the ratio force to length in each branch [3]. The latter is an effective tool to solve multi-constrained problems of structural optimization, especially when used in conjunction with augmented Lagrangian approaches [4].

A classical formulation of optimization for elastic structures consists in the minimization of the structural compliance for a given amount of material. In this research this formulation will be endowed with additional sets of constraints to avoid structural collapse, due to yielding and buckling, and to meet geometric/manufacturing prescriptions. While yielding can be straightforwardly avoided by means of constraints at a local level, i.e. controlling the magnitude of the force in each branch [5], buckling must be carefully prevented considering both local and global instability. When a topology optimization problem is considered, i.e. when form-finding is coupled to the research of an optimal distribution of possibly vanishing cross-sections, singularity issues must be taken into account. Moreover, nodal instability may occur [6]. Suitable approaches will be tested to control the structural behavior in compression, mainly relying on energy-based methods [7] or eigenvalue-based approaches [8]. A standard optimization setting with continuous minimization variables will be considered. Suitable manufacturing constraints will be addressed to enforce limitations concerning the geometry of the design domain and/or the set of minimization variables. In more detail, the adoption of projection techniques will be considered to accommodate a discrete set of cross-sections, for instance related to a selection of available profiles or to the adoption of a given nozzle in additive manufacturing. 

The equilibrium will be investigated at first in the case of deterministic loading. The effect of probabilistic loads will be considered using Monte Carlo simulation, first order (FORM), second order (SORM, ) approaches and ad hoc formulations which allow to control the probability of failure through equivalent deterministic constraints [9,10, 11].