Optimal design of steel structures according to the Eurocodes using mixed-integer linear programming methods

In structural design, achieving minimum cost is the main goal. Structural design optimization plays a crucial role in reaching this goal. It can reduce both the consumption of natural resources by the construction industry and the engineering effort and therefore cost by automation of some of the most repetitive tasks in the design process. However, practicing structural engineers are reluctant to adopt optimization as a daily design tool. One of the reasons is that real-world design problems are often governed by a number of practical constraints prescribed by the building codes. Some of these constraints are non-smooth, therefore most existing design optimization algorithms cannot take into account all these practical constraints. In addition, the optimization problem contains discrete design variables since the member profiles have to be chosen from a catalog of commercially available alternatives.

This doctoral thesis presents a new method to find the global solution of truss, frame, and combined truss-frame discrete sizing optimization problems. The adopted approach is to reformulate the optimization problem as a Mixed-Integer Linear Programming (MILP) problem. In order to facilitate the reformulation of the optimization problem as an MILP, the simultaneous analysis and design approach is adopted: the state variables, such as the internal forces, are considered as additional design variables and the state equations, such as the equilibrium equations and member stiffness relations, are enforced by means of additional constraints. In addition, a set of binary decision variables is introduced for each member of the structure to select a profile from the catalog given by the designer. The obtained MILP can be solved for global optimality with well-established algorithms such as branch-and-bound methods.

The optimized designs are required to meet the requirements prescribed by the Eurocodes, which are design rules developed by the European Committee for Standardization. Because of the complexity of these constraints, usually only member and displacement constraints are taken into account during the optimization. In this doctoral thesis, not only the Eurocode constraints related to member strength and stability but also all Eurocode constraints related to the joints of the structure are taken into account. As a consequence, a post-processing step to account for other constraints is avoided, therefore optimality is retained and additional engineering time is avoided.

The results show that the developed method can solve discrete optimization problems of moderate scale including all relevant Eurocode constraints and reaching global optimality. Furthermore, the importance of taking all Eurocode constraints into account during the optimization is demonstrated.