Formulation of a thin shell finite element with continuity C 0 and convected material frame notion

 This paper presents a formulation for a new family of thin shell finite elements. The element is formulated by using a convected material frame notion which offers an interesting framework to take into account large transformations. Bending behaviour is calculated from the Love–Kirchhoff assumptions and from a finite difference technique between adjacent elements. We therefore called this element SFE for semi-finite-element. This method allows us to keep C ⁰ continuity without introducing other variables than the 3 classical displacements, which reduces computational time. In this paper, a full formulation of this element is described more precisely. It takes into account the coupling effect between both membrane and bending behaviour. Various sample solutions that illustrate the effectiveness of the element in linear and nonlinear analysis are presented, with some sheet metal forming examples. Received 10 January 2001