PSI - Issue 32

Andrey Yu. Fedorov et al. / Procedia Structural Integrity 32 (2021) 194–201 A.Yu. Fedorov et al. / Structural Integrity Procedia 00 (2021) 000–000

198

5

b

a

0.00163970

70.5

0.00163965

70

 x  P x

 x  P x

0.00163960

69.5

0.00163955

69

0.00163950

68.5

0 50000 100000 150000 200000

0 50000 100000 150000 200000

Number of elements

Number of elements

Fig. 4. Dependences of stresses σ x on the substrate surface on the number of elements of the finite-element mesh at t / t 1 = 10 for di ff erent ratios of the plate and substrate elastic moduli: a) E / E 1 = 0 . 001; b) E / E 1 = 1000.

a

b

Fig. 5. Patterns of strain distribution ε x on the plate surface at t / t 1 = 10, E / E 1 = 0 . 1, ν = ν 1 = 0 . 3: a) without substrate; b) with substrate.

In our calculations, the characteristic size of elements near the substrate that corresponds to that of the mesh with 54000 elements for t / t 1 = 10. Figure 5 shows the strain distributions ε x on the plate surface with and without a substrate at t / t 1 = 10, E / E 1 = 0 . 1, ν = ν 1 = 0 . 3 and under load P x = 1, P y = 0. These results show that the embedding of a substrate has a rather significant e ff ect on the redistribution of strains.

4. Results

Changes in the strain fields caused by the installation of the substrate will be defined by the following quantity:

ε x 0 − ε x 1 ε x 0

100% ,

(3)

·

δ x =

where ε x 0 is the strain ε x at the center of the plate (without the substrate), ε x 1 is the strain ε x at the center of the outer surface of the substrate.