Parametric Optimization of Thin-Walled 3D Beams with Perforation Based on Homogenization and Soft Computing

Abstract

The production of thin-walled beams with various cross-sections is increasingly automated and digitized. This allows producing complicated cross-section shapes with a very high precision. Thus, a new opportunity has appeared to optimize these types of products. The optimized parameters are not only the lengths of the individual sections of the cross section, but also the bending angles and openings along the beam length. The simultaneous maximization of the compressive, bending and shear stiffness as well as the minimization of the production cost or the weight of the element makes the problem a multi-criteria issue. The paper proposes a complete procedure for optimizing various open sections of thin-walled beam with different openings along its length. The procedure is based on the developed algorithms for traditional and soft computing optimization as well as the original numerical homogenization method. Although the work uses the finite element method (FEM), no computational stress analyses are required, i.e., solving the system of equations, except for building a full stiffness matrix of the optimized element. The shell-to-beam homogenization procedure used is based on equivalence strain energy between the full 3D representative volume element (RVE) and its beam representation. The proposed procedure allows for quick optimization of any open sections of thin-walled beams in a few simple steps. The procedure can be easily implemented in any development environment, for instance in MATLAB, as it was done in this paper.

Optimal Design of Bubble Deck Concrete Slabs: Sensitivity Analysis and Numerical Homogenization

“…Although the procedure presented in this work has not been experimentally verified, the homogenization method itself, used in the presented procedure, has already been verified on various engineering examples in our previous works [ 35 , 36 , 39 , 40 , 41 ]. The proposed algorithm can of course be implemented in a completely different computing environment; however, the procedure should be consistent with the diagram presented in Figure 4 and the general design guidelines presented in the previous paragraph.…”

Effective Stiffness of Thin-Walled Beams with Local Imperfections

“…The main advantage of thin-walled sections is that their application allows for the optimal use of the construction material [ 9 ]. The relation of the load-bearing strength to weight of this construction element is high, compared to other typical steel structures from hot-rolled elements, such as I-beams, rectangular, or square pipes.…”

“…In the literature, there are various homogenization methods. One approach uses the equivalent of the deformation energy [ 9 , 17 , 18 , 19 , 20 , 21 ]. The authors of this paper wrote several papers regarding the numerical homogenization technique for plates, which were based on a concept from Biancolini [ 17 ].…”

“…Moreover, it has been shown that the homogenization technique can be used in structural optimization to efficiently obtain solutions. In [ 9 ], the geometrical parameters of the thin-walled cross-section were sought by using surrogate models without losing the accuracy of the calculation results. Not only the structural parameters may be optimized but also the material [ 22 , 23 ] or the topology of the structure [ 24 , 25 ].…”