Multi-objective structural optimization of shallow domes considering geometric nonlinearity and grouping of bars

Resumo

The formulation and solution of structural optimization problems in trusses is broadly discussed in the literature, commonly involving objective functions such as minimizing the structure's weight and nodal displacements. In most of these works, the structures present elastic and geometrically linear behavior. In this paper, a multi-objective structural optimization problem (MOSOP) is proposed, involving objective functions such as minimizing the weight of the structure, maximizing the first natural frequency of vibration, maximizing the critical load factor related to the global stability and minimizing the number of distinct cross-sectional areas of the bars, simplifying, for instance, the manufacturing, assembling, checking, welding, etc.. The constraints are related to the maximum nodal displacements. The analyzed structure is a shallow dome with geometric nonlinearity. Therefore, a geometrically nonlinear analysis is performed to determine the deformed configuration of the structure, using the cylindrical arc-length method. This analysis allows the designer to obtain more accurate values for the objective functions and constraints. Three evolutionary algorithms are applied to solve the MOSOP, and their performances and solutions are compared. The Pareto front obtained in the proposed problem is presented, for example, illustrating how the growth of the dome's weight leads to increases in the first critical load factor and the first natural frequency of vibration. It is also possible to note how the structural weight can be reduced by grouping bars with a higher number of distinct cross-sectional areas. Finally, optimized solutions are extracted from the Pareto front based on the decision-maker's preferences.