Optimization of steel castellated and cellular beams using finite element method and genetic algorithms

Resumo

The quest to consume resources more consciously and effectively encourages the use of optimization
processes. In this sense, the present study aims to employ computational optimization techniques to determine the
maximum strength of open-web steel beams, for two groups of different cut lines, one generating beams with holes
in the hexagons-shape and another in ellipse format. From these two models of cut lines, a set of parameters is
defined that establish different configurations for the cut line in an analyzed I-shaped profile, for example: distance
between holes; position along the web height; hole dimensions; among others. A computational routine is
implemented to generate, from the analyzed I-shaped profile and for certain parameter values, a finite element
mesh. The load capacity of the castellated and cellular beam is defined through a nonlinear analysis using the finite
element program FEMOOP and a three-node triangular finite element in plane stress state. This element was
chosen due to the need for a very refined mesh in the discretization process of the different possible configurations
of cut lines, therefore, the finite elements are small and do not require high degree interpolating functions. The
optimization process consists of defining, for a given I-shaped profile, which configuration of the cut line produces
a castellated or cellular beam with greater load capacity. The implemented routines are validated from numerical
and experimental models found in the literature, and it is expected, from an analysis of the beams found in the

populations obtained by the evolution of the genetic algorithm, an increase in the load capacity of the analyzed I-
shaped profile.