ANALYSIS OF A 3-DIMENSIONAL PROBLEM OF THE THEORY OF ELASTICITY FOR AN INHOMOGENEOUS TRUNCATED HOLLOW CONE

The three-dimensional stress-strain state of an inhomogeneous thin tru ncated hollow cone is studied by the method of direct asymptotic integ ration of the equations of the theory of elasticity [1]. Assuming that the load is sufficiently smooth, inhomogeneous solutions are construc ted, which enable the load to be removed from the lateral surface of t he cone. Homogeneous solutions are then constructed. Asymptotic expans ions of homogeneous solutions are obtained, which enable the stress-st rain state to be computed under various boundary conditions on the end s of the cone. The nature of the stress-strain state is clarified by a qualitative analysis. It is shown that, as in the homogeneous case [2 ], the stress-strain state consists of three types: the internal stres s state, the simple boundary effect, and the boundary layer.