Formulation of a thin shell finite element with continuity C0 and convected material frame notion

Abstract

International audienceThis 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

Modeling and analysis of in-plane bending in fibrous reinforcements with rotation-free shell finite elements.

“…The rise of commercial calculation codes in the 1990s led to the development of finite elements with a relatively simple formulation and a limited number of degrees of freedom for sake of efficiency. The S3 element is part of a category of shell elements called rotation free like the BPT element developed by (Oñate and Zárate, 2000) or as developed in (Laurent and Rio, 2001). The S3 element is a triangular element with linear shape functions, having three degrees of freedom in translation at each node of the element.…”

Optimal Deployment Control of Spinning Space Webs and Membranes

“…Cirak et al [21] use subdivision surfaces, which are extended to large deflections [20]. Rio et al [84] develop a shell element which takes into account both large displacements and coupling effects between membrane and bending behaviour. This element uses isoparametric interpolation in an attempt to model constant curvatures normal to each edge, which leads to problems in finding suitable integration points.…”

“…This can be done using a co-rotational formulation. • Eventually, develop an RF shell element that takes into account the coupling of bending and membrane effects as the element by Rio et al [84], but use constant curvatures over the whole patch as Phaal and Calladines element. However, some of the simplicity with the element would then be lost.…”

Numerical study of dynamic relaxation with kinetic damping applied to inflatable fabric structures with extensions for 3D solid element and non-linear behavior

“…Its invariants are then used to define the potential and its different variations, needed for the calculation of Cauchy's stress tensor [21].…”

“…The deformation is calculated from the variation of the coordinates of the metric tensor associated to the material coordinates of the point in the reference element (a comprehensive example of this calculus has been presented in [21]). Then, the stress tensor is obtained by means of the formulae Spheric part :…”