Multi-objective structural optimization of a planar truss considering dy- namic and global stability aspects

Resumo

The literature has broadly discussed the development of multi-objective structural optimization prob-
lems (MOSOPs) with two objectives: minimizing the structure’s weight and the maximum nodal displacement.

This paper proposes the formulation of MOSOPs with three objective functions. New objectives are considered,
such as the maximization of the first natural frequency of vibration and the maximization of the difference between
the second and the first ones, to avoid the superposition of their modes. MOSOPs are also proposed to maximize
the first critical load factor related to the structure’s global stability and the difference between the second and the
first ones. The analyzed structure is a 10-bar truss. The design variables are the cross-sectional areas of the bars.

The evolutionary algorithm is the third step of generalized differential evolution (GDE3). The Pareto fronts ob-
tained for the problems are presented. It is possible to observe how the growth of the truss’ weight causes increases

in the first natural frequency of vibration and the first critical load factor, as well as its influence on the differences
between the frequencies of vibration and the critical load factors of the structure. Finally, optimized solutions are
extracted from the obtained Pareto fronts.