Abstract
This paper presents a method to find the global solution of combined truss-frame size optimization problems. The approach is based on a reformulation of the optimization problem as a Mixed-Integer Linear Programming problem (MILP) which is solved by means of a branch-and-bound method. A portal frame that consists of both beam and truss elements is adopted as a test case. The optimal sections of the portal frame have to be selected from a square hollow sections catalog. The design of the portal frame has to meet the requirements prescribed by the Eurocodes. These requirements are adopted as constraints by reformulating them as or approximating them by a linear equation. 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 during the optimization. As a consequence, a post-processing step to account for other constraints is avoided, therefore optimality is retained and additional engineering time is reduced. The optimization results are presented and the influence of the joint constraints on the optimal design is discussed. In addition, the efficiency of the method is compared with the efficiency of a genetic algorithm.
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Van Mellaert, R., Mela, K., Tiainen, T., Heinisuo, M., Lombaert, G., Schevenels, M. (2018). Mixed-Integer Linear Programming Reformulation Approach for Global Discrete Sizing Optimization of Trussed Steel Portal Frames. In: Schumacher, A., Vietor, T., Fiebig, S., Bletzinger, KU., Maute, K. (eds) Advances in Structural and Multidisciplinary Optimization. WCSMO 2017. Springer, Cham. https://doi.org/10.1007/978-3-319-67988-4_56
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DOI: https://doi.org/10.1007/978-3-319-67988-4_56
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