PSI - Issue 32

Daria Dolgikh et al. / Procedia Structural Integrity 32 (2021) 246–252 D. Dolgikh, M. Tashkinov / Structural Integrity Procedia 00 (2019) 000–000

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4

( ) ( ) { } [ ] e K p x u f   =  

(3)

where [ ] f is a vector of volumetric surface forces, ( ) ( ) e K p x     is a structural global stiffness matrix, obtained by the assemblage of element stiffness matrix over the design domain, ( ) e p x - is the density of each element in the computational domain, determined by Equation 4: ( ) ( ) e e E x p x E = (4) where E is the elastic modulus for the given isotropic material, which assumed to be the same for all elements, ( ) e E x is optimal stiffness tensor reaching isotropic material properties. 3. Results and discussion Some results of numerical optimization of the studied RVEs according to the formulated problem are shown in the figures below. a b

Fig.3. Mises stress distribution field in a representative volume (p = 0.5) of the cellular structure a) before optimization; b) after optimization . a b

Fig.4. Mises stress distribution field in a representative volume (p = 0.512) of the cellular structure a) before optimization; b) after optimization.