PSI - Issue 79

Victor Rizov et al. / Procedia Structural Integrity 79 (2026) 109–116

114

loads induced by the normal and tangential accelerations. Therefore, the distribution of the strain in a cross-section of the structural member is presented by Eq. (31). y z z y C     = + + , (31) where

2 b h y b −   , h −   . z 2

(32)

2 (33) Here, C  is the strain in the cross-section centre, y  and z  are the curvatures in the planes, xy and xz , respectively, y and z are the horizontal and vertical centric axes of the cross-section. Equations (34), (35) and (36) are used to determine the strain in the cross-section centre and the two curvatures.  = ( ) A N dA  , (34)  = ( ) A y zdA M  , (35)  = ( ) A z M ydA  , (36) where A is the cross-section area, N is the axial force, y M and z M are the bending moments generated by the distributed inertia loads. The SERR found by Eq. (29) is confirmed by the solution given in Eq. (37) (Rizov ( 2017)). 2

1 b

  

   ,

− A u dA u dA u dA +  ( ) A   ( ) 1 * 0 ( ) 2 A * 02 * 01

G

=

(37)

where *

* 02 u and * 0 u are the complementary strain energy densities in the upper and lower arms of the crack

01 u ,

behind the crack tip and in the structure ahead of the crack tip, respectively. 3. Parametric analysis

Here we analyze the effect of various parameters of the model of the structure rotating around motionless horizontal axis on the longitudinal fracture. In this relation, the solution of the SERR is applied. The following data are used in the analysis: 0.300 = a m, 0.015 = b m, 0.025 = h m, 1.200 1 = l m, 0.600 2 = l m, 0.5 = m  , 0.6 =   , 0.7 = R  and 0.8 = r  . The effects of the length of the vertical member of the rotating structure and the variation of material properties, R , along the length of the structure on the longitudinal fracture are studied first. The length of the vertical member of the rotating structure and the variation of material property, R , are characterized by 1 2 / l l and 1 4 / L L R R ratios, respectively. Figure 3 gives an idea about the change of the SERR (the latter is expressed in non-dimensional form by using the formula ( ) G R b L 1 / ) induced by increase of 1 2 / l l ratio at different 1 4 / L L R R ratios. The quick rise of the SERR when 1 2 / l l ratio grows can be explained by increase of the normal and tangential accelerations (Fig. 3). The reduction f the SERR with growth of 1 4 / L L R R ratio that one can observe in Fig. 3 is a consequence of increase of the structure stiffness. The influence of the parameter,  , and the variation of material property,  , along the length of the structure on the longitudinal fracture is studied too. The variation of  is characterized by 4 1 / L L   ratio. The study resulted in