Vibrations of complex shells of revolution using B-spline finite elements

This paper presents and evaluates a local–global B-spline finite element method for the modal analysis of joined thin shells of revolution. Each shell component is modelled by a super element. For smooth meridian, local displacements of the shell middle surface and their first derivatives are matched at the junction. However, for discontinuous shells, the C1 continuity of tangential displacements is relaxed and a local to global frame transformation is applied for normal and longitudinal displacements. The super element formulation in local–global frame reference and the minimum number of degrees of freedom (three nodal displacements augmented by the bending rotation at the joints only), provided by the uniform cubic B-spline interpolation, are the main originalities of the present work. Efficiency and accuracy of the proposed technique are evaluated through various well known two-branch shell combinations. Results are compared to analytical, experimental and numerical solutions found in the literature. A very satisfactory behaviour of the approach was observed.