The displacement solution of conical shell and its application

Abstract

In this paper, the displacement solution method of the conical shell is presented. From the differential equations in displacement form of conical shell and by introducing a displacement function, U(s, θ), the differential equations are changed into an eight-order soluble partial differential equation about the displacement function U(s, θ) in which the coefficients are variable. At the same time, the expressions of the displacement and internal force components of the shell are also given by the displacement function. As special cases of this paper, the displacement function introduced by V. Z. Vlasov in circular cylindrical shell, the basic equation of the cylindrical shell and that of the circular plate are directly derived.

Under the arbitrary loads and boundary conditions, the general bending problem of the conical shell is reduced to finding the displacement function U(s, θ), and the general solution of the governing equation is obtained in generalized hypergeometric function. For the axisymmetric bending deformation of the conical shell, the general solution is expressed in the Bessel function.

On the basis of the governing equation obtained in this paper, the differential equation of conical shell on the elastic foundation (A Winkler Medium) is deduced, its general solutions are given in a power series, and the numerical calculations are carried out.