PSI - Issue 59

Hryhorii Habrusiev et al. / Procedia Structural Integrity 59 (2024) 494–501 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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of contact stresses are observed at the center of contact domain. The appearance of plane part leads to a shift of the extreme points to the edge of contact domain and decreases their absolute value.

Fig. 4 . Distributions of contact stresses ( a ) and vertical displacements ( b ) for various values of layer thickness

  * r  describing the distribution of contact stresses for the case of

In fig. 4 a ) shows a graph of a function

pressure on a layer lying without friction on a rigid base, a parabolic indenter at 2 R  , 0 a r  . A graph of the quantity   * u r describing the vertical displacements of the points of the upper boundary plane of the layer for the same case is constructed in fig. 4 b ). Dotted curve shows the case of pressure of the indenter on the half-space (Habrusiev et al, 2022), curve 1 corresponds to the pressure of a similar indenter with the same force on the layer thickness 0.5 h  , curve 2 – 1 h  , curve 3 – 2 h  . As can be seen from the figures already at 2 h  , ie if the thickness of the layer is twice the radius of the contact area, the distribution of contact stresses is close to the corresponding distribution for half-space. That is, a further increase in the thickness of the layer will not lead to a significant reduction in contact stresses. The solved problems and the conclusions made on their basis can be used for the purpose of economy of material at manufacturing of a plate, without reducing its durability.

Fig. 5. Extreme values of contact stresses and vertical displacements

In fig. 5 illustrates the dependence of the extreme values of contact stresses and vertical displacements of the points of the upper boundary plane of the layer in the case of pressure of the parabolic indenter. Curves 1 correspond to an incompressible layer with the available Bartenev-Khazanovich elastic potential, and curves 2 to a compressible layer with a harmonic type potential. All curves are constructed for the case 1 P E  , 2 R  , 0 a r  .