NONLINEAR TRANSIENT-RESPONSE OF IMPERFECT HYPERBOLIC SHELLS USING A REDUCTION METHOD

The paper analyzes the effect of geometric imperfections on the free-vibration, and static and dynamic responses of hyperbolic shells. The effect of geometric nonlinearities is included. A 48 degree-of-freedom thin shell element, capable of modeling arbitrary geometric imperfections, is employed. A reduced basis method using the normal modes as the base vectors is employed to reduce the size of the nonlinear problem and thus save computational effort. The resulting reduced (but still coupled) set of equations is integrated in a step-by-step fashion using the Wilson-0 method along with an iterative scheme. The integration scheme, first evaluated on a series of examples (both linear and nonlinear) is employed to obtain the dynamic response of hyperbolic shells with geometric imperfections. The shell is subjected to wind loads with an assumed time history. The results are presented for the nonlinear static response of a cooling tower under wind loads; for the fundamental frequencies of a hyperbolic shell under increasing axisymmetric pressure loads; and finally for the dynamic response (normal displacements and the in-plane stress resultants) of an example hyperbolic shell under dynamic wind loads. Whenever possible, the present results are compared with those available in the existing literature. A good agreement is observed.