Abstract

A family of rotation-free three node triangular shell elements is presented. The simplest element of the family is based on an assumed constant curvature field expressed in terms of the nodal deflections of a patch of four elements and a constant membrane field computed from the standard linear interpolation of the displacements within each triangle. An enhanced version of the element is obtained by using a quadratic interpolation of the geometry in terms of the six patch nodes. This allows to compute an assumed linear membrane strain field which improves the in-plane behaviour of the original element. A simple and economic version of the element using a single integration point is presented. The efficiency of the different rotation-free shell triangles is demonstrated in many examples of application including linear and non
linear analysis of shells under static and dynamic loads, the inflation and de-inflation of
membranes and a sheet stamping problem.

Abstract

A new triangle shell element is presented. The advantages of this element are threefold: simplicity, generality and geometrical accuracy. The formulation is free from rotation degrees of freedom. The triangle here presented can be used regardless of the mesh topology, thus generality is conserved for any meshrepresented surface. From an original first order approach we evolve to a third order geometric description. The higher degree geometric description is based on the Bézier triangles concept, a very well known geometry in the domain of CAGD [G. Farin, Curves and Surfaces for CAGD. A Practical Guide, fifth ed., Morgan Kaufmann Publishers, San Francisco, CA, 2002]. Using this concept we show the path to reconstruct a general third order interpolating surface using only the three coordinates at each node. This work takes as starting point the nodal implementation of a basic triangle shell element [E. Oñate, F. Zárate, Rotation-free triangular plate and shell elements, Int. J. Numer. Methods Engrg. 47 (2000) 557– 603]. In order to use an exact formula for the curvature, the normal directions at each node and the way to characterize them are proposed. Then, the geometrical properties and the mechanical behavior of the surface created are introduced. Finally, different examples are presented to depict the versatility and accuracy of the element.

Abstract

The paper describes how the finite element method and the finite volume method can be successfully combined to derive two new families of thin plate and shell triangles with translational degrees of freedom as the only nodal variables. The simplest elements of the two families based on combining a linear interpolation of displacements with cell centred and cell vertex finite volume schemes are presented in detail. Examples of the good performance of the new rotation‐free plate and shell triangles are given.

Abstract

This paper presents a formulation for analysis of thin elastic membranes using a rotation-free shell element within an explicit time integration strategy. The applications presented are isotropic/anisotropic rectangular membranes under shear forces and fabric drapes falling over a pedestal. Results are compared with other numerical results existing in the literature.