A complete set of eigensolutions is constructed for different variants of circular conical bodies: homogeneous cone with one lateral surface (solid cone), homogeneous cone with two lateral surfaces (hollow cone) and composite cone for different variants of boundary conditions on the lateral surface. It has been shown that the constructed eigensolutions can be readily applied for estimation of the character of stress singularity at the vertices of conical bodies. The character of stress singularity at the vertex of the solid and hollow cones for different variants of boundary conditions on the lateral surfaces has been defined by direct numerical simulations. Numerical results obtained for solid, hollow and compose cones under different boundary conditions on the lateral surfaces are discussed.
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