Three-dimensional static and dynamic analyses of truncated conical shells by a modified scaled boundary finite element method

The purpose of this paper is to develop a semi-analytical numerical method for investigating the static and dynamic mechanical properties of circular conical shells. The mathematical model is formulated using a modified scaled boundary finite element method (SBFEM) based on three-dimensional elastic theory in a circular conical coordinate system. With the modified SBFEM, the inner surface of conical shell is chosen as scaling plane, unlike the conventional SBFEM, which uses a scaling center to model the geometry of the computational domain, so that this approach accurately describes the geometry of conical shells without introducing discrete errors. At the same time, the modified SBFEM retains the advantage of the conventional method, where only the boundaries of the computational domain need to be discretized, while an analytical solution can be obtained in the radial direction of the conical shell. Based on the principle of virtual work, a second-order differential governing SBFEM equation with variable coefficients is derived for the structure, marking the most significant difference from classical SBFEM. The static bending, free vibration and transient dynamic responses of conical shells are then calculated using the precise integration method. The accuracy and applicability of the present method are verified by comparing the numerical results with those obtained from the software ANSYS and the literature. The effects of geometrical parameters, boundary conditions and loading types on displacement, stress and frequency are also investigated. The numerical results indicate that these variables have a significant impact on the response of the conical shell structure.