Keywords: mono-dimensional model, spherical shell, long and short dams, linear static behaviour..

In spherical shells, as a result of the axial-symmetry of the system, all the quantities involved in the elastic problem only depend on the curvilinear abscissa along the meridian lines. Hence, the mathematical domain of the model becomes monodimensional. However, in the classical model of axial-symmetric spherical shells, the kinematic problem is not the adjoint of the static problem. With the aim of clarifying this aspect, a mono-dimensional linear model of axial-symmetric spherical shells has been proposed. The adopted mono-dimensional approach furnishes a model where the kinematic problem is the adjoint of the static problem. This model, which is able to describe the linear static behaviour of the shell, can be considered as a curved beam resting on an elastic variable soil. Specifically, the axis of the generic curved beam coincides with a meridian line and the elastic soil is related to the characteristics of the ring beams along the parallel lines. Several internal constraints and simplifying assumptions have been introduced. The comparison between the approximate analytical models and a finite element model confirm the effectiveness of the proposed monodimensional approach. The most approximate model permits a closed-form solution. It appears to be perfectly capable of describing the classical oscillatory-damped behavior of beams on elastic soil. For this reason it has been used to introduce a criterion to classify spherical shells as long or short. Graphs, that permit a handy classification, are then proposed, depending only on the geometrical characteristics of the shell.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £65 +P&P)