Higher-order hybrid-mixed axisymmetric thick shell element for vibration analysis

In this study, we present free vibration analysis of shells of revolution using the hybrid-mixed nite element. The present hybrid-mixed element, which is based on the modi ed Hellinger{Reissner variational principle, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees to resolve the numerical di culties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out by the Guyan reduction. Several numerical examples show that the present element with cubic displacement interpolation functions and consistent quadratic stress functions is highly accurate for the free vibration analysis of shells of revolution, especially for higher vibration modes