PSI - Issue 28

Boris N. Fedulov et al. / Procedia Structural Integrity 28 (2020) 155–161 Fedulov B., Fedorenko A., Jurgenson S., Kantor M., Lomakin E. / Structural Integrity Procedia 00 (2019) 000–000

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1. Introduction Constructions works has no essential innovations for the century, nevertheless general advances in science; engineering and technology let us perform new construction elements, which can essentially speed up building process, increase quality and reliability of structures. Currently, usage of concreate slabs enforced by metal bars has its limit, because of high weight of concreate and price for additional metal reinforcements. Usual options for modernization: using new concreate, which is locally enforced by any type of fibers (fiber-reinforced concrete); and replacements of metal bars by pultruded composite ones – stumble on fire safety regulations, and cannot be used for the most of the structures. This fact pushes authors to search the solution for improvement in the usage of conventional metal enforcements with new optimal shape. This research presents new type of enforcements for construction slab with higher strength and stiffness characteristics. 2. Optimization of enforcements One of the most critical load case for construction concreate slab is the bending for the horizontal floor propose. It is mostly evident that for maximum stiffness of plate we need to put some material on the top of concreate and on the bottom, to have maximum for the moment of inertia. Next question is the connection of these two layers and adhesion with concreate. For this problem we use modern optimization method known as topology optimization [1], with relaxed statement, where density of the material ρ can take intermediate values between no material ( 0   ) and full of material ( 1   ) points of optimized structure.

Fig. 1. Solid body divided by sub regions with volume Ω n .

For an arbitrary solid elastic body, which divided into n sub regions with volumes Ω n (fig. 1), formal statement of problem for maximum stiffness with restriction to mass has the form:

1 2        Ω , , ..., min ={ n ij ijkl kl E d 

Ω,

},

(1)

0 p E E   ijkl n ij

,

kl



Ω

i 

,

M



0

i

n