Solution of static problems for a three-dimensional elastic shell

摘要

A study was conducted to find a solution of static problems for a three-dimensional elastic shell. The shell of a constant thickness h was considered where the middle surface Ω was related to the curvilinear orthogonal coordinates θ_1 and θ_2 counted along the principal-curvature lines. A variational equation was the basis for constructing the geometrically exact bilinear finite element of the shell. The term 'geometrically exact' meant that the shell middle surface was described by analytically set functions. The analytical integration was used within the limits of a finite element, which was the prerogative of the geometrically exact shell element.