Free vibration analysis of arbitrary thin shell structures by using spline finite element

This paper presents the free vibration analysis of arbitrary thin shell structures by using a newly developed spline finite element. The new element has three salient features in its formulation: (i) the use of B-spline shape functions for the interpolations of both in-plane and out-of-plane displacements of a general thin shell element; (ii) the use of “displacement constraints” and “parameters shifting” to construct a finite element model; (iii) that a proposed modified version of the Koiter’s thin shell theory is employed. The element is doubly curved, has nine primary nodes and eight auxiliary nodes, and has a total of 63 degrees of freedom. It is formulated through the conventional C 1displacement approach, and is capable of modelling sharp corners, arbitrary shapes and multiple junctions of thin shell structures. The numerical examples discussed include spherical panels, cylindrical panels and shells of revolution, as well as single- and double-cell boxes. These examples are typical shells of negative, zero and positive Gaussian curvatures. The effects of aspect ratios, distorted meshes and junctions of shells on the performance of the element are studied. It is shown that the new spline finite element is a reliable, versatile, accurate and efficient thin shell element suitable for the analysis of arbitrary thin shell structures.