Calculation of Shells of Revolution with the Use of a Mixed FEM with a Vector Approximation Procedure

Abstract

A finite element algorithm in a mixed formulation has been developed to find stresses and displacements occurring in a shell of revolution. The finite discretization element has been taken in the form of a curvilinear quadrangle of the middle shell surface. As the nodal unknowns in the mixed formulation, forces and moments inherent in the middle surface with a bilinear approximation have been used, as have the displacements and their first derivatives in two approximation variants of the sought kinematic quantities in scalar and vector form. By the example of calculations, the efficiency has been shown for the approximation of the sought kinematic quantities as vector fields, and it has been noted that the determination of stresses occurring in shells of revolution made of incompressible materials is quite possible.