Global Size Optimization of Statically Determinate Trusses Considering Displacement, Member, and Joint Constraints

Abstract

Realistic truss design optimization problems are often governed by practical constraints. Because of the complexity of these constraints, usually only member constraints are taken into account during the optimization, and joint constraints are accounted for in a manual postprocessing step. This paper proposes a method to account for joint constraints in the global discrete size optimization of a steel truss structure. The design of an N-type truss girder is considered first without and then with the joint constraints specified in the Eurocode. To guarantee global optimality in both cases, the optimization problem is reformulated as a mixed-integer linear program. A statically determinate analysis model is adopted so as to ensure that all joint constraints can be reformulated as linear functions. If the joint constraints are not considered in the optimization, a design is obtained where the joints need additional strengthening. This can be done by manually selecting heavier sections, which often leads to a suboptimal result, or by strengthening the joints (e.g., by means of stiffening plates), which has a serious effect on the fabrication cost. If the joint constraints are considered in the optimization, they are automatically satisfied by the final design. The weight of this design is about 15% higher than in the first case. This shows that the joint constraints have a significant effect on the optimal design. If the joint constraints are accounted for in a suboptimal way (e.g., by manually selecting heavier sections), the additional weight may be even higher. Taking into account joint constraints in the optimization leads to a cost reduction at two levels: in terms of engineering cost (no manual postprocessing step is needed) and fabrication cost (using unnecessarily heavy sections and joint strengthening are avoided).