Agrupamento ótimo de barras de pórticos espaciais de aço via otimização estrutural multi-objetivo

Abstract

Structural optimization problems considering structures composed of bars, such as trusses and frames, are mostly formulated by defining weight (volume or mass) as the primary objective function in their formulations. This optimization can be classified as dimensional or parametric, where the design variables are the characteristics of the cross sections; shape, where the structure’s contours or geometric characteristics are assigned as design variables; topological, when the presence or absence of structural elements is considered as design variables; and, finally, all of them considered simultaneously. Constraints usually refer to maximum nodal displacements, maximum stresses, minimum natural vibration frequencies, buckling loads, among others. In most cases, problems are formulated with a single objective, which is the weight to be minimized. On the other hand, when more than one objective is of interest to the designer, other functions are introduced into the formulations, such as minimizing the maximum displacement, maximizing natural vibration frequencies, or maximizing critical load factors. These objectives can also be considered simultaneously in the same formulation. In the context of structural optimization involving bar structures, an interesting possibility is to obtain optimized structures that take into account the groupings of bars according to the designer’s expectations. These groupings provide gains in manufacturing, assembly, checking, execution, architectural aspects, the labor economy, and so on. The task of finding the optimal groupings is not trivial and may require the designer’s experience, as well as trial-and-error processes that can be costly. In the literature, proposed strategies include automatic bar grouping as constraints imposed in the formulation of structural optimization problems. One of them is the consideration of cardinality constraints. In the context of optimal bar grouping, this master thesis proposes the formulation of a multi-objective structural optimization problem of spatial frames considering the weight of the structure and the number of distinct bars (columns and beams) as clearly conflicting objective functions. In this proposal, three experiments are carried out in which the conflict between grouping and weight is analyzed. First, the operation of the grouping methodology is tested and validated. Next, automatic grouping is proposed to be verified in analyses of symmetry and asymmetry of the structure and a pre-grouping analysis. In all problems, a Differential Evolution-based algorithm was used.