Shell Finite Element Formulated on Shell Middle Surface

Abstract

A four‐noded quadrilateral pure shell element based on the thin‐shell theory of Koiter (1966) has been developed. The element, having a variable number of nodal degrees of freedom with a maximum of 12, is formulated on the plane reference domain by a mapping of the curved shell middle surface from the three‐dimensional space. Any arbitrary global coordinate system can be used due to the implementation of tensorial coordinate transformation. Excellent behavior of the element is observed when tested against a set of severe benchmark tests. The benchmark tests demonstrate that the element is able to handle rigid‐body motion without straining, inextensional modes of deformation, complex membrane strain states, and skewed meshes. The two‐dimensional interpolation functions are formed from the tensor product of Lagrange and Hermitian one‐dimensional interpolation functions, and the order of interpolation can be varied.