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Topology design of vlasov beam sections

Çetin, Fatih
The optimal cross-section of beams plays an important role in load carrying members. The section of a beam should be designed such that the structure carries higher loads with less weight. Some structures which are subjected to static combined loading require a continuous cross-section along their axial direction due to manufacturing reasons. In classical structural topology optimization methods, it is aimed to optimize the whole beam. However, these methods are impractical when optimize the whole beam as they generate beams with non-uniform topologies and varying cross-sections along the axial direction. On the other hand, most of the earlier studies address only the bending and torsional rigidity optimization of cross-sections, regardless of the loading on the beam in question. In this thesis, the topology optimization of Vlasov beam sections is studied according to Vlosov beam theory. For the purpose of this study an optimization method hereby known as the Evolutionary Growth Algorithm (EGA) was generated and through this algorithm it is proposed that the optimum cross-section can be found in accordance with the strength to area ratio. The optimization methodology generated in this thesis uses element Von Mises stress as a material addition and removal criterion and also takes symmetrical design constraints into account. Indeed, material addition and/or removal are decided according to the stress level of each element and the symmetry constraints of the cross-section. The cross section domain has to be coherent throughout its evolution, i.e. there should be no disconnection between the elements. Therefore, a special algorithm is included in the Evolutionary Growth Algorithm (EGA) to check the connectivity of the active elements in the cross-section during element removal. At the end of the optimization process, it is aimed to have determined the optimum cross-section limit at which point the area will be minimized for the maximum Von Misses stress applied to the section. Both finite element analyses and optimization algorithm were coded in MATLAB and run consecutively to achieve the goal of this study.