PSI - Issue 81

Leonid Voytovych et al. / Procedia Structural Integrity 81 (2026) 287–291

289

b

c

a

Fig. 2. Slicing scheme: (a) meridional slices; (b) slices perpendicular to the meridional ones; (c) slices perpendicular to the hole axis

3. Results and discussion Thin plate (the plate deflection exceeds one-fifth of its thickness). The distributions of stresses σ R and σ θ along the plate radius in the unweakened zone on the tensile and compressed surfaces are shown in Fig. 3a . As can be seen from the results obtained, the stresses σ R and σ θ at opposite points located on the tensile and compressed surfaces differ in magnitude. This is explained by the fact that the resulting stress state is a superposition of bending and membrane stresses. The distribution of the calculated membrane stresses σ R М and σ θ М is presented in Fig. 3b (experimental results are indicated by symbols, calculated values by solid lines).

a

b

Fig. 3. Stress distributions: (a) σ R and σ θ along the radius; (b) membrane stresses σ R М and σ θ М

The distributions of circumferential stresses σ φ along the hole contour on the tensile and compressed surfaces of the plate are shown in Fig. 4a . On the tensile contour, the maximum σ φ stresses occur at points 1 (5), whereas on the compressed contour they occur at points 3 and 7, indicating the presence of four maxima. Figure 4a also shows the distributions of σ φ along the hole generators passing through points 1 (5), 3, and 7. The dist ribution of σ φ stresses through the plate thickness is linear. Table 2 presents the stress concentration factors at points 1 (5), 3, and 7. These factors are defined as the ratio of the stresses σ φ at the corresponding points to the stresses in the unweakened zone of the plate.

Table 2. Stress concentration coefficients. № contour points

Contour is compressed ( K ) Contour is stretched ( K )

p. 1(5)

1.3 1.6 2.0

2.7

p.3 p.7

1.35

1.9

Moderately thick plate (the plate deflection does not exceed one-fifth of its thickness). The distributions of stresses σ R and σ θ along the plate radius in the unweakened zone on the tensile and compressed surfaces are shown in Fig. 4b by symbols. Solid lines represent the calculated stress distributions for a circular plate under bending. The difference between experimental and calculated stresses reaches up to 15%. This discrepancy can be attributed to the presence of the central loading pin. The distributions of