Finite Element Weighted Residual Methods: Axisymmetric Shells

The shell thickness and the shell reinforcement both may vary along the meridian of the shell, but they must remain constant around the circumference of the shell. The shell may be subjected to pressure and to thermal effects that may be nonsymmetrically distributed around the shell circumference and vary along the shell meridian. The analysis is based upon thin shell theory that utilizes the Love-Kirchhoff approximation. By means of Fourier expansions in the circumferential coordinate, the partial differential equations of equilibrium of the shell are reduced to ordinary differential equations in the meridional coordinate. For each Fourier harmonic, numerical solutions of the reduced equations are obtained by means of finite element weighted residual methods. A finite element model of the displacement field along the meridian is constructed by means of piecewise cubic Hermite polynomials. Three different weighted residual methods, i.e., subdomain collocation, Galerkin, and moments, are used to generate element stiffness matrices and load vectors.