New rotation-free finite element shell triangle accurately using geometrical data

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 mesh-represented 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.