Issue 49

V. Matveenko et alii, Frattura ed Integrità Strutturale, 49 (2019) 225-242; DOI: 10.3221/IGF-ESIS.49.23 227 The case when 1 0   corresponds to a solid cone. Figure 1 : Hollow cone (a); composite cone (b). We state the problem of constructing eigensolutions, which will satisfy the homogeneous equations of equilibrium (1 ) 0 S grad div rot rot    u u (2) (here 1/1 2 S n = - , n is Poisson's ratio, u is the displacement vector) and homogeneous boundary conditions at the surfaces 1 0 , q q q q = = for displacements 0, 0, 0 r u u u      (3) and stresses 0, 0, 0 r          (4) or mixed boundary conditions, which in the context of solid mechanics correspond to a perfect- slip boundary condition at the lateral surface 0, 0, 0 r u         (5) For the examined body of revolution and boundary conditions (3)-(5), the eigensolutions can be represented as a Fourier series [20] in the circumferential coordinate                          0 0 0 1 1 1 , , sin , , v v sin , , cos r w k k k k k k u r u r u r k u r r r k u r w r r k                                                   (6) Here the dependence on the radius is expressed according to (1), , , r u u u   -are the components of the displacement vector along the , , r   -axes, , , r       are the components of the stress tensor,  is the characteristic index.