Issue 49

V. Matveenko et alii, Frattura ed Integrità Strutturale, 49 (2019) 225-242; DOI: 10.3221/IGF-ESIS.49.23 236 where 1 2 3 4 5 6 , , , , , C C C C C C are the constants defined by the prescribed combination of boundary conditions (3) –( 5). E XAMPLE OF CALCULATION OF CHARACTERISTIC INDICES FOR CONICAL BODIES he general solutions obtained for 0 k  and 1 k  under the prescribed combination of the boundary conditions were used to construct a homogeneous system of algebraic equations with respect to constants i C for the examined conical body. The coefficients of this system of equations depend on the vertex angles of conical bodies, elastic characteristics of the materials and characteristic index  . The indices  , defining the character of stress singularity at the vertices of conical bodies are calculated from the condition of the existence of non-zero solution to the system of linear algebraic equations. Solid cone Let us consider a solid cone ( 0 0 , 0 , 0 r           ). For this case, in general solutions (32), (37), (45) it is necessary to retain terms with particular solutions (15) at 0 x  (or 0   ). Subject to this condition the solutions take the following form: axisymmetric rotation ( 0 k  )     (1) (1) 0 0 0 w x C w x   (46) axisymmetric deformation ( 0 k  )             (1) (1) (2) (2) 0 0 0 0 0 (1) (1) (2) (2) 0 0 0 0 0 , u x C u x C u x v x C v x C v x         (47) non-axisymmetric deformation ( 0 k  )                       (1) (1) (2) (2) (5) (5) (1) (1) (2) (2) (5) (5) (1) (1) (2) (2) k k k k k k k k k k k k k k k k k k k u x C u x C u x C u x v x C v x C v x C v x w x C w x C w x                 (48) The substitution of these solutions in one of the boundary conditions (3)–(5) at 0 q q = yields a system of linear homogeneous algebraic equations for the unknown quantities, (1) (2) (1) (2) (5) 0 0 , , , , k k k C C C C C , which have the following representation: axisymmetric rotation ( 0 k  ) (1) (1,1) 0 0 0 C   (49) axisymmetric deformation ( 0 k  ) (1) (1,1) (2) (1,2) 0 0 0 0 (1) (2,1) (2) (2,2) 0 0 0 0 0, 0. C C C C             (50) non-axisymmetric deformation ( 0 k  ) T