Axisymmetric Problem of Stressed State for a Twice Truncated Cone

Abstract

We consider an axisymmetric mixed problem of stressed state for a twice-truncated cone with regard for its own weight and the conditions of smooth contact imposed on its conical surface. The application of a new integral transformation with respect to the meridian angle directly to the Lame equations reduces the problem in the space oftransforms to a one-dimensional vector boundary-value problem. The obtained problem is solved exactly with the help of the methods of matrix differential calculus. The subsequent application of the inverse integral transformations gives the final solution of the original problem. We study the solutions in special cases of the formulated problem, such as a cone with spike, a spherical dome, and a half ball. We also determine the normal stresses acting on the surface of the cone depending on its geometric parameters.