Eight-node quadrilateral double-curved surface element for membrane analysis

The dynamic relaxation method is applied to membrane analysis using an eight-node quadrilateral element. The element uses second order shape functions to approximate the geometry of the structure. The element is based on the element of Gosling and Lewis [Gosling PD, Lewis WJ. Optimal structural membranes—I. Formulation of a curved quadrilateral element for surface definition. Comp Struct 1996;61:871–83]. They used a finite element approach. In this paper exact tensorial calculation is used to determine the exact deformation between the deformation-free state and the actual state.