Construction of a homogeneous solution to the elasticity theory problem for an inhomogeneous truncated transversally isotropic cone

Using an asymptotic integration method, this paper investigates the axisymmetric problem of elasticity theory for inhomogeneous transversal-isotropic truncated cone small thickness. It is believed that moduli are arbitrary continuous functions opening angle. assumed lateral part free stresses, and boundary conditions set at ends cone, leaving it in equilibrium. Homogeneous solutions have been constructed, is, all to equilibrium equations satisfy condition absence stresses on surfaces cone. Three groups were derived: a penetrating solution, such as simple edge effect, well layer solutions. An analysis stressed-strained state was carried out. shown solution having character effect determine internal Solutions localized its first terms equivalent Saint-Venant plate. A particular type thickness with degeneration median surface into plane has studied. case special, consist nature layer. Asymptotic formulas derived make possible calculate On basis obtained solutions, build new refined applied applicability existing theories conical shells. New classes identified no can describe