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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where ij  - is the Cauchy stress, ij  -elastic deformations, p -dimensionless constant, 0 defines a set of material stiffness moduli, M 0 – target mass of the structure. Density distribution ρ n is a function of coordinates and if the point of the medium has coordinate x lying inside the element with index n, then ρ n (x)= ρ n if (x ⊂ Ω n ). For our particular problem, we used two load cases – applying bending moments in two direction (fig. 2). Object function for optimization was a sum of two compliances taken from two elastic solutions. Plate dimension is 5m×5m×0.23m. i jkl E is a fourth-rank tensor that

Fig. 2. Two load cases for optimization . The main parameter for this optimization task is the target mass M 0 , which was chosen as 10% of initial mass of optimization region. Well known algorithm of steepest descent [1, 2] was used for minimization of objective function. Each iteration has its own set of densities, which can be visualized by removing of material with small values of ρ (for example ρ<0.3). Fig.3 shows stages of optimization and corresponding changes of material shape.

Fig. 3. Stages of optimization.

The proposed by optimization algorithm shape of reinforcements is too complex, however we can get the main idea - angled sticks, which make shear transfer from outer layers to each other in the most strict way. Fig. 4 shows the proposed structure of reinforcements inspired by optimization results. It consist of two outside layers and a set of pyramid type supports, which connect these main covers.