No abstract

The dynamic response of hyperboloidal shells on discrete column supports is studied using a curved rotational shell finite element. In this finite element formulation, the displacement field over each element domain is approximated by polynomial functions in which the coefficients of the linear terms correspond to the nodal values of the displacements and the higher order terms vanish at the nodal circles. The stiffness and mass matrices associated with the equations of motion are derived from Hamilton's variational principle and include the effects of transverse shearing deformation and rotatory inertia. Since the formulation, as such, involves a great many degrees of freedom because of the use of higher order displacement functions, the kinematic condensation technique is employed to reduce the order of the dynamic problem The dynamic analysis indicates the importance of realistically modelling the base region of the shell. Studies on a prototype tower indicates that the base flexibility reduces the natural frequencies of the shell and increases the displacements near the base. The magnitude of this reduction, which could be significant, depends primarily on the tangential stiffnesses of the supporting columns and is hardly affected by the thickened ring beam at the base.

The computation of stresses within a finite element displacement method analysis of a shell of revolution is considered. The common procedure of applying the kinematic and constitutive laws to the displacement functions is examined and justified for models where the displacements are represented by high‐order polynomial expansions. Also, two alternative computational formats within this technique are explored. The influence of the column‐supported base condition on a hyperboloidal shell of revolution is studied with respect to the stresses calculated from a response spectrum analysis. These studies emphasize the importance of accurately modelling the base region of a column‐supported shell such as a hyperbolic cooling tower.