Otimização de estruturas em aço treliçadas

Abstract

In the most cases, the structural engineer defines an initial configuration based on yours experiences for the structural system to be designed and, through iteratives processes, check if the technical standarts conditions for the security and service are satisfy. Even though the propused solution satisfies the the conditions, it may not be the best in consumption of materials terms. For the optimal solution, is necessary to use structural optimization technics, able to provide designs increasingly lighter and time and materials savings. The objective of the present work is the development of algorithms for minimizing the weight of trussed steel structures, based on differents optimization methods (mathematics and heuristics). Compare the efficiency between the Sequential Quadratic Programming (SQP) and the Genetic Algorithm, taking into account the quality of the solutions found, the complexity of implementation and the computational cost required. The results show that, when using the technical standarts for compressed bars, it is necessary to adopt bars with more robust cross sections when compared to solutions whose restrictions derive from the classic formulation of Euler's critical load. A similarity between the results obtained by the SQP and the Genetic Algorithm is observed, but due to the combinatorial nature of the latter, the heuristic method requires longer processing time. In addition, the results obtained by the Genetic Algorithm are shown to be random during the iterations, and may converge in slightly heavier solutions than the SQP. Justified by the results presented, it is stated that the developed algorithms are good tools for structural optimization and can be used in real steel truss designs.