An efficient, conforming axisymmetric shell element including transverse shear and rotary inertia

A conforming, two-node conical element is presented incorporating both transverse shear deformation and rotary inertia effects. The success of the formulation is based on the C⁰ continuity shape functions that, in addition to providing full kinematic compatibility, satisfy the interdependent variable interpolation requirement. This requirement points toward a particular dependence of the kinematic variable interpolations which allow for the satisfaction of the Kirchhoff constraint everywhere in the element domain. There exists an internal degree-of-freedom reduction achieved by means of a continuous shear constraint condition. In the derivation of element matrices, Hamilton's principle is invoked with Gaussian quadratures ensuring exact integration throughout. Excellent convergence characteristics and high accuracy results attainable with the element are demonstrated in static and free vibration problems for thin and moderately thick plates and shells.